# Statistics Assignment questions and answers

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1. A_______ is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.

- significance level
- parameter
- test statistic
- critical value

**Answer:- test statistic**

2. The test statistic measures how close the computed sample statistic has come to the hypothesized population parameter.

- True
- False

**Answer:- True**

3. If the p-value is less than alphaα in a two-tail test, _______.

- a one-tail test should be used
- the null hypothesis should be rejected
- no conclusion should be reached
- the null hypothesis should not be rejected

**Answer:- the null hypothesis should be rejected**

4. The larger the *p-*value, the more likely you are to reject the null hypothesis.

- True
- False

**Answer:- False**

5. The smaller the *p-*value, the stronger is the evidence against the null hypothesis.

- True
- False

**Answer:- True**

6. Which of the following would be an appropriate null hypothesis?

- The sample proportion is less than 0.65.
- The population proportion is less than 0.65.
- The sample proportion is no less than 0.65.
- The population proportion is not less than 0.65.

**Answer:- The population proportion is not less than 0.65.**

7. Which of the following would be an appropriate alternative hypothesis?

- The mean of a population is greater than 55.
- The mean of a population is equal to 55.
- The mean of a sample is greater than 55.
- The mean of a sample is equal to 55.

**Answer:- The mean of a population is greater than 55.**

8. Which of the following would be an appropriate alternative hypothesis?

- The sample proportion is less than 0.65.
- The population proportion is less than 0.65.
- The population proportion is not less than 0.65.
- The sample proportion is not less than 0.65.

**Answer:- The population proportion is less than 0.65.**

9. An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W. From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W. A consumer group has decided to try to discover if the claim appears true. They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.

What are the appropriate hypotheses to determine if themanufacturer’s claim appears reasonable?

- H00:μ≤250 and H11: μ>250
- H00: μ=250 and H11: μ≠250
- H00: μ≥257.3 and H11: μ<257.3
- H00: μ≥250 and H11:μ<250

**Answer:- H00:μ≤250 and H11: μ>250**

10. A drug company is considering marketing a new local anesthetic. The effective time of the anesthetic the drug company is currently producing has a normal distribution with a mean of 7.4 minutes with a standard deviation of 1.2 minutes. The chemistry of the new anesthetic is such that the effective time should be normally distributed with the same standard deviation, but the mean effective time may be lower. If it is lower, the drug company will market the new anesthetic; otherwise, they will continue to produce the older one. A sample of size 36 results in a sample mean of 7.1. A hypothesis test will be done to help make the decision.

Which of the following are the appropriate hypotheses?

- H00: μ>7.4 and H11: μ≤7.4
- H00: μ≥7.4 and H11: μ<7.4
- H00: μ≤7.4 and H11: μ>7.4
- H00: μ=7.4 and H11: μ≠7.4

**Answer:- H00: μ≥7.4 and H11: μ<7.4**

11. A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 15 to 19. If the same sample had been used to test the null hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the mean of the population differs from 20, the null hypothesis could be rejected at a level of significance of 0.05.

- True
- False

**Answer:- True**

12. A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 15 to 19. If the same sample had been used to test the null hypothesis that the mean of the population is equal to 18 versus the alternative hypothesis that the mean of the population differs from 18, the null hypothesis could be rejected at a level of significance of 0.05.

- True
- False

**Answer:- False**

13. It is possible to directly compare the results of a confidence interval estimate to the results obtained by testing a null hypothesis if

- a two-tail test for μ is used.
- a one-tail test for μ is used.

**Answer:- I only**

14. You have created a 95% confidence interval for μ with the result 10≤μ≤15. What decision will you make if you test H00: μ=16 versus H11: μs≠16 at αs=0.05?

- Do not reject H00 in favor of H11.
- Reject H00 in favor of H11.
- Fail to reject H00 in favor of H11.
- We cannot tell what our decision will be from the information given.

**Answer:- Reject H00 in favor of H11.**

15. You have created a 95% confidence interval for μ with the result 10≤μ≤15. What decision will you make if you test H00: μ=16 versus H11: μs≠16 at αs=0.10?

- Do not reject H00 in favor of H11.
- Reject H00 in favor of H11.
- Fail to reject H00 in favor of H11.
- We cannot tell what our decision will be from the information given.

**Answer:- Reject H00 in favor of H11.**

16. An economist wishes to determine whether there is evidence that mean family income in a community exceeds $50,000. Which of the following statements is correct?

- Either a one-tail or two-tail test could be used with equivalent results.
- A two-tail test should be utilized.
- A one-tail test should be utilized.
- None of the above.

**Answer:- A one-tail test should be utilized.**

17. The owner of a local nightclub has recently surveyed a random sample of n=250 customers of the club. She would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. What are the appropriate hypotheses to test?

**Answer:- >H00: μ≤30 and H11: μ>30**

18. The owner of a local nightclub has recently surveyed a random sample of n=250 customers of the club. She would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. If she wants to have a level of significance at 0.01, what rejection region should she use?

- Reject H00 if t<−2.5758.
- Reject H00 if t>2.3263.

**Answer:- Reject H00 if t>2.3263.**

19. In a hypothesis test, it is irrelevant whether the test is a one-tail or two-tail test.

- True
- False

**Answer:- False**

20. A proper methodology in performing hypothesis tests is to ask whether a random sample can be selected from the population of interest.

- True
- False

**Answer:- True**

21. "What conclusions and interpretations can you reach from the results of the hypothesis test?" is not an important question to ask when performing a hypothesis test.

- True
- False

**Answer:- False**

22. "Is the intended sample size large enough to achieve the desired power of the test for the level of significance chosen?" should be among the questions asked when performing a hypothesis test.

- True
- False

**Answer:- True**

23. In conducting research, you should document both good and bad results.

- True
- False

**Answer:- True**

24. An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W. From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W. A consumer group has decided to try to discover if the claim appears true. They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.

Which of the following is the parameter of interest?

- 250
- 257.3
- the mean power consumption of the 20 microwave ovens
- the mean power consumption of all such microwave ovens

**Answer:- the mean power consumption of all such microwave ovens**

25. The quality control engineer for a furniture manufacturer is interested in the mean amount of force necessary to produce cracks in stressed oak furniture. She performs a two-tail test of the null hypothesis that the mean for the stressed oak furniture is 650. The calculated value of the *Z* test statistic is a positive number that leads to a *p-*value of 0.080 for the test. If the test is performed with a level of significance of 0.10, the null hypothesis would be rejected.

- True
- False

**Answer:- True**

26. For all two-sample tests, the sample sizes must be equal in the two groups.

- True
- False

**Answer:- False**

27. The sample size in each independent sample must be the same if one is to test for differences between the means of two independent populations.

- True
- False

**Answer:- False**

28. When you test for differences between the means of two independent populations, you can only use a two-tail test.

- True
- False

**Answer:- False**

29. A statistics professor wanted to test whether the grades on a statistics test were the same for upper and lower classmen. The professor took a random sample of size 10 from each, conducted a test and found out that the variances were equal. For this situation, the professor should use a t test with related samples.

- True
- False

**Answer:- False**

30. If one is testing for the difference between the means of 2 independent populations presuming equal variances with samples of n1=20 and n2=20, what is the number of degrees of freedom?

**Answer:- 38**

31. In testing for the differences between the means of 2 independent populations where the variances in each population are unknown but assumed equal, how many degrees of freedom are there?

- n−1
- n−2
- n1+n2−1
- n1+n2−2

**Answer:- n1+n2−2**

32. In testing for differences between the means of two independent populations, what is the null hypothesis?

- H00: μ1−μ2>0
- H00: μ1−μ2=2
- H00: μ1−μ2=0
- H00: μ1−μ2<2

**Answer:- H00: μ1−μ2=0**

33. Are managers from Country B more motivated than managers from Country A? A randomly selected group of each were administered a survey which measures motivation for upward mobility. The survey scores are summarized below.

Country A |
Country B | |

Sample Size |
211 |
100 |

Sample Mean SSATL Score |
65.75 |
79.83 |

Sample Std. Dev. |
11.07 |
6.41 |

Give the null and alternative hypotheses to determine if the mean survey score of managers from Country B differs from the mean survey score of managers from Country A.

**Answer:- H00: μA−μB=0 H11: μA-μB≠0**

34. If one is testing for the difference between the means of 2 related populations with samples of n1=20 and n2=20, what is the number of degrees of freedom?

- 19
- 38
- 18
- 39

**Answer:- 19**

35. In testing for differences between the means of 2 related populations where the variance of the differences is unknown, how many degrees of freedom are there?

A. n1+n2−2 B. n−2 C. n1+n2−1 D. n−1

**Answer:- n−1**

36. A drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training. To test whether any improvement occurred, the instructor would use a t distribution with 11 degrees of freedom.

- True
- False

**Answer:- False**

37. In testing for differences between the means of two related populations, the null hypothesis is which of the following?

**Answer:- H0: μD=0**

38. When testing for differences between the means of 2 related populations, you can use either a one-tail or two-tail test.

- True
- False

**Answer:- True**

39. A researcher is curious about the effect of sleep on students' test performances. He chooses 60 students and gives each two tests, one given after two hours' sleep and one after eight hours' sleep. The test the researcher should use would be a related samples test.

- True
- False

**Answer:- True**

40. If you wish to determine whether there is evidence that the proportion of items of interest is higher in group 1 than in group2, which test is appropriate touse?

**Answer:- The Z test for the difference between two proportions**

41. In testing the difference between two proportions using the normal distribution, you may use a two-tail Z test.

- True
- False

**Answer:- True**

42. A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let π1 and π2 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively. If the firm wanted to test whether this proportion has changed from the previous study, which represents the relevant hypotheses?

**Answer:- H0:π1−π2=0 H11: π1−π2≠0**

43. The statistical distribution used for testing the difference between two population variances is the________ distribution.

**Answer:- F**

44. The test for the equality of two population variances is based on which of thefollowing?

**Answer:- The ratio of the 2 sample variances**

45. The F test used for testing the difference in two population variances is always aone-tail test.

- True
- False

**Answer:- False**

46. What can be concluded if the computed F statistic is greater than the critical F value in aone-way ANOVA?

**Answer:- Reject H0 since there is evidence that not all the means are equal.**

47. How is the F test statistic in a one-way ANOVA calculated?

**Answer:- MSA/MSW**

48. How are the degrees of freedom for the F test in a one-way ANOVA calculated?

**Answer:- (c−1) and (n−c)**

49. In aone-way ANOVA, what is always true about the nullhypothesis?

**Answer:- There is no difference in the population means.**

50. When the F test is used for ANOVA, the rejection region is always in the right tail.

- True
- False

**Answer:- True**

51. When comparing the mean sales among 3 different brands view the results from a three-way ANOVA design.

- True
- False

**Answer:- False**

52. The F test in a completely randomized model is just an expansion of the t test for independent samples.

- True
- False

**Answer:- True**

53. If we wish to determine whether there is evidence that the proportion of items of interest is the same in group 1 as in group 2, the appropriate test to use is _______.

**Answer:- both the Z test and the χ2 test**

54. In testing a hypothesis using the χ2 test, the theoretical frequencies are based on which of the following?

**Answer:- null hypothesis**

55. A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let π1 and π2 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.

If the firm wanted to test whether this proportion has changed from the previous study, which represents the relevant hypotheses?

**Answer:- H0: π1−π2=0 and H1:π1−π2≠0**

56.In testing the difference between two proportions using the normal distribution, we may use either a one-tail Chi-square test or two-tail *Z *test.

- True
- False

**Answer:- True**

57.A test for the difference between two proportions can be performed using the chi-square distribution.

- True
- False

**Answer:- True**

58. The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day. He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors. In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the accounting majors are designated as "Group 1" and the economics majors are designated as "Group 2," perform the appropriate hypothesis test using a level of significance of 0.05.

Which of the following hypotheses should the dean use?

**Answer:- H0: π1-π2=0 and H1: π1-π2≠0**

59. If the χ2 method of analysis is used to test for the differences among 4 proportions, the degrees of freedom are equal to ___.

**Answer:- 3**

60. When using the χ2 tests for independence, you should be aware that expected frequencies that are too small will lead to a large Type I error.

- True
- False

**Answer:- True**

61. The chi-square test of independence requires that the expected frequency in each cell to be at least 5.

- True
- False

**Answer:- False**

62. The chi-square test of independence requires that the expected frequency in each cell to be at least 1.

- True
- False

**Answer:- True**

63. The squared difference between the observed and theoretical frequencies should be large if there is no significant difference between the proportions.

- True
- False

**Answer:- False**

64. A computer used by a24-hour banking service is supposed to randomly assign each transaction to one of 5 memory locations. A check at the end of aday's transactions gave the counts shown in the table to each of the 5 memory locations, along with the number of reported errors.

The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ. What is the critical value of the test statistic at 1% level of significance, rounded to four decimal places?

**Answer:- 13.2767**

65. The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ. What is the calculated value of the test statistic, rounded to four decimal places?

**Answer:- 1.4999**

66. The bank manager wanted to test whether the proportion of errors in transactions assigned to each of the 5 memory locations differ. Which test would be used to properly analyze the data in this experiment?

**Answer:- χ2 test for difference among more than two proportions**

67. According to an article in anewspaper, fewer checks are being written at the grocery store checkout than in the past. To determine whether there is a difference in the proportion of shoppers who pay by check among three consecutive years at a 0.05 level ofsignificance, the results of a survey of 500 shoppers in three consecutive years are obtained and presented in the contingency table.

Referring to Scenario 12-6, what is the form of the null hypothesis?

**Answer:- H0:π1=π2=π3**

68. What is the form of the alternativehypothesis?

**Answer:- H1: not all πj are the same**

69. Data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given in the contingency table.

At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities. The decision made suggests that the 3 cities all have different proportions of hotels that correctly post minibar charges.

- True
- False

**Answer:- False**

70. At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities. There is sufficient evidence to conclude that the proportions between City A and City B are different at a 0.05 level of significance.

- True
- False

**Answer:- True**

71. Many companies usewell-known celebrities as spokespersons in their TV advertisements. A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent. Each in a sample of 300 female TV viewers was asked to identify a product advertised by a celebrity spokesperson. The gender of the spokesperson and whether or not the viewer could identify the product was recorded. The numbers in each category are given in the contingency table.

What is the number the degrees of freedom for the test statistic?

**Answer:- 1**

72. One criterion used to evaluate employees in the assembly section of a large factory is the number of defective pieces per1,000 parts produced. The quality control department wants to find out whether there is a relationship between years of experience and defect rate. Since the job isrepetitious, after the initial training period any improvement due to a learning effect might be offset by a loss of motivation. A defect rate is calculated for each worker in a yearly evaluation. The results for 100 workers are given in the table.

What is the expected number of employees with less than 1 year of training time and a high defect rate?

**Answer:- 5.28**

73. Recent studies have found that American children are more obese than in the past. The amount of time children spent watching television has received much of the blame. A survey of 100ten-year-olds revealed the following with regards to weights and average number of hours a day spent watching television. We are interested in testing whether the mean number of hours spent watching TV and weights are independent at1% level of significance.

What is the degrees of freedom of the test statistic?

**Answer:- 4**

74. What does the Y-intercept (b0) represent?

**Answer:- The Y-intercept (b0) represents the predicted value of Y when X=0.**

75. What does the slope (b1) represent?

**Answer:- The slope (b1) represents the estimated average change in Y per unit change in X.**

76. The results of the simple linear regression are provided below. Interpret the estimate of β0, the *Y-*intercept of the line.* *

Y =minus−2,700plus+20*X*, *S*YX=65, two-tail p-value=0.034 (for testing β1)

**Answer:- There is no practical interpretation since a sales revenue of$0 is a nonsensical value**

77. What does it mean when a simple linear regression model is "statistically" useful?

**Answer:- The model is a better predictor of Y than the sample mean, Y.**

78. The least squares method minimizes which of the following?

**Answer:- SSE**

79. What does the coefficient of determination (*r*2) signify?

**Answer:- The proportion of total variation that is explained**

80. The coefficient of determination represents the ratio of SSR to SST.

- True
- False

**Answer:- True**

81. The standard error of the estimate is a measure of which of the following?

**Answer:- The variation around the sample regression line.**

82. In performing a regression analysis involving two numerical variables, you are assuming which of the following statements?

- That the variances of
*X*and*Y*are equal. - That the variation around the line of regression is the same for each
*X*value. - That
*X*and*Y*are independent.

**Answer:- II only**

83. Data that exhibit an autocorrelation effect violate the regression assumption of independence.

- True
- False

**Answer:- True**

84. The residuals represent which of the following?

**Answer:- The difference between the actual Y values and the predicted Y values.**

85. If the plot of the residuals is fan shaped, which assumption is violated?

**Answer:- Homoscedasticity**

86. Regression analysis is used for prediction, while correlation analysis is used to measure the strength of the association between two numerical variables.

- True
- False

**Answer:- True**

87. If the correlation coefficient (*r*) is equal to 1.00, then which of the following must be true?

**Answer:- There is no unexplained variation.**

88. If the correlation coefficient (*r*) is equal to 1.00, then which of the following must be true?

**Answer:- All the data points must fall exactly on a straight line with a positive slope.**

89. Assuming a linear relationship between *X* and *Y*, if the coefficient of correlation (*r*) is equal to minus−0.30, then which of the following must be true?

**Answer:- The slope ( b1) is negative.**

90. The strength of the linear relationship between two numerical variables may be measured by which of the following?

**Answer:- The coefficient of correlation**

91. In a simple linear regression problem, which of the following must be true about *r* and *b*1?

**Answer:- They must have the same sign.**

92. When *r*=minus−1, it indicates a perfect relationship between *X* and *Y*.

- True
- False

**Answer:- True**

93. A zero population correlation coefficient between a pair of random variables means that there is no linear relationship between the random variables.

- True
- False

**Answer:- True**

94. The management of a chain electronic store would like to develop a model for predicting the weekly sales(in thousands ofdollars) for individual stores based on the number of customers who made purchases. A random sample of 12 stores yields the results shown in the accompanying table. Which is the correct null hypothesis for testing whether the number of customers who make a purchase affects weekly sales?

**Answer:- H0: β1=0**

95. It is believed that GPA(grade pointaverage, based on a four point scale) should have a positive linear relationship with ACT scores. Given below is the technology output for predicting GPA using ACT scores based a data set of 8 randomly chosen students from a university.

Which of the following is true about the value of the measured (observed) test statistic of the *F-*test for *H*0:

β1=0 vs. *H*1: β1≠0?

**Answer:- It is always positive.**

96. The confidence interval for the mean of *Y *is always narrower than the prediction interval for an individual response *Y* given the same data set, *X* value, and confidence level.

- True
- False

**Answer:- True**

97. A large national bank charges local companies for using their services. A bank official reported the results of a regression analysis designed to predict the bank's charges (*Y*), measured in dollars per month, for services rendered to local companies. One independent variable used to predict service charges to a company is the company's sales revenue (*X*), measured in millions of dollars. Data for 21 companies who use the bank's services were used to fit the model: *Y**i*=β0+β1*X*i+E*i*. The results of the simple linear regression are provided below.* *

*Y*=−2,700+20*X*, *S*YX=65, two-tail *p-*value=0.034 (for testing β1)

Interpret the estimate of σ, the standard deviation of the random error term (standard error of the estimate) in the model.

**Answer:- About95% of the observed service charges fall within$130 of the least squares line.**

98. It is believed that, the average numbers of hours spent studying per day during undergraduate education should have a positive linear relationship with the starting salary, measured in thousands of dollars per month, after graduation. Given below is the technology output for predicting starting salary (*Y*) using number of hours spent studying per day (*X*) for a sample of 51 students. What is the error sum of squares (SSE) of the accompanying regression?

**Answer:- 92.0325465**

99. Which of the following assumptions can be made based on the residual plot to theright? (only graph)

**Answer:- Homoscedasticity**

100. A computer software developer would like to use the number of downloads(in thousands) for the trial version of his new shareware to predict the amount of revenue(in thousands of dollars) he can make on the full version of the new shareware. Use the accompanying simple linear regression along with the residual plot and normal probability plot, obtained from a data set of 30 different sharewares, to determine whether the statement is true or false.

Answer:- False

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