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BUSN1009 The Study Large Rural Town

A population has a mean of 150 and a standard deviation of 21. If a random sample of 49 is taken, what is the probability that the sample mean is:

  1. less than 147
  2. between 152.5 and 157.5
  3. between 148 and 158?

Question 2 

A random sample of 81 is drawn from a population with a standard deviation of 12. If a sample mean greater than 300 is obtained only 18% of the time, what is the mean of the population?

Question 3

For a population with p=0.6, find the probability for each sample proportion and given sample size.

  1. n = 100 and
  2. n = 240 and

Question 4

A population proportion is .32. Suppose a random sample of 40 items is sampled randomly from this population. What is the probability that the sample proportion is:

  1. between .18 and .51
  2. between .38 and .48

Question 5

According to a study undertaken in a large rural town, 15% of children aged from 10 to 16 years old were found to exercise less than one hour per day. If a random sample of 35 children in this age group was selected from this town, what is the probability that more than 7 children would be found to exercise less than one hour per day?

Question 6 

According to a study, the average travel time to work in Perth is 27.4 minutes. A business researcher wants to estimate the average travel time to work in Brisbane using a 95% level of confidence. A random sample of 45 Brisbane commuters is taken and the travel time (minutes) to work is obtained from each. The data follow. Assuming a population standard deviation of 5.124 minutes, compute a 95% confidence interval on the data. What is the point estimate and what is the margin of error of the interval? Explain what these results mean in terms of Perth commuters.

27

25

19

21

24

27

29

34

18

29

16

28

20

32

27

28

22

20

14

15

29

28

29

33

16

29

28

28

27

23

27

20

27

25

21

18

26

14

23

27

27

21

25

28

30

 

 

 

Question 7 

Assuming x is normally distributed, use the following data to compute a 90% confidence interval to estimate µ.

313

320

319

340

325

310

321

329

317

311

307

318

Question 8

Use the information about each of the following samples to compute the confidence interval to estimate p.

  1. n = 25 and = .24; 98% confidence interval
  2. n = 213 and = .38; 95% confidence interval
  3. n = 62 and = .73; 80% confidence interval

Question 9

A candidate is considering nominating for an election to become Mayor of a country town. Prior to officially nominating, the candidate decides to conduct a survey to assess the chances of being elected. Ninety voters are randomly selected with 55 indicating they will vote for the candidate. Find a 95% confidence interval for the proportion of voters in the town that will vote for this candidate. Based on this confidence interval, can the candidate determine whether or not to nominate for the election to become Mayor.


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