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STA10003 Foundations of Statistics And Management

Questions:

Question 1

The variable ‘anticlot’ indicates the type of anti-clotting drug prescribed to the patients.Produce the relevant graph and table to summarise the ‘anticlot’ variable and write a report describing this variable in the style presented in the course materials.

Question 2

The age of patients in years is provided in the data file. Produce the relevant graph and tables to summarise the ‘age’ variable and write a report describing this variable in the style presented in the course materials.

Question 3

Current research indicates that the number of everyday life stressors has risen in the last decade. Hospital records for 2014 show that 74% of Australians admitted to hospital for suspected myocardial infarction had normal blood pressure at the time of admission. The researchers have suggested, that due to increasing stress, the percentage of Australians admitted to hospital for suspected myocardial infarction who have normal blood pressure at the time of admission is now lower than this.

Conduct a Binomial Test using the ‘bp ’ variable to test the researchers’ hypothesis. Produce the relevant output and write a Binomial test report based on your output in the style presented in the course materials.

Question 4

Due to federal cuts to the Government Health System, the researchers predicted that the average length of stay in hospital for patients admitted for suspected myocardial infarction is now lower than the average of 5.5 days recorded in 2014.

Conduct a One-Sample t-test using the ‘los’ variable to test this prediction. Produce the relevant output and write a One-sample t-test report based on your output in the style presented in the course materials.

Question 5

The researchers have also claimed that the average length of stay in hospital for patients who have a history of diabetes is higher than the average for those who do not. Conduct an Independent samples t-test using the ‘los’ and ‘diabetes’ variables to investigate this claim. Produce the relevant output and write an Independent samples t-test report based on your output in the style presented in the course materials.

Answers:

Question 1

The variable ‘anticlot’ indicates the type of anti-clotting drug prescribed to the patients.

Produce the relevant graph and table to summarise the ‘anticlot’ variable and write a report describing this variable in the style presented in the course materials.

Solution

In this question, the study sought to understand the most frequent type of anti-clotting drug prescribed to the patients. Table 1 below gives the frequency distribution of the various types of anti-clotting drugs prescribed to the patients. It can be seen that the most prescribed drug is Aspirin (42%, n = 844) while the least prescribed drug is Warfarin (7%, n =148).  22% (n = 442) of the patients did not receive any drug prescription while 27% (n = 544) of the patients were


prescribed for Heparin.

Table 1: Type of anti-clotting drug prescribed

 

 

Frequency

Percent

Valid Percent

Cumulative Percent

Valid

Aspirin

844

42.2

42.7

42.7

Heparin

544

27.2

27.5

70.2

Warfarin

148

7.4

7.5

77.7

None

442

22.1

22.3

100.0

Total

1978

98.9

100.0

 

Missing

System

22

1.1

 

 

Total

2000

100.0

 

 

The above results can also be visualized in the bar chart presented in figure 1 below;

Figure 1: Bar chart of anti-clotting drugs prescribed to the patients

Question 2

The age of patients in years is provided in the data file.

Produce the relevant graph and tables to summarise the ‘age’ variable and write a report describing this variable in the style presented in the course materials.

Solution

The average age of the patients in years was found to be 63.45 years with oldest patient being 95 years old while the youngest patient was 45 years old.

Table 2: Descriptive statistics

 

Age in years

N

Statistic

1995

Range

Statistic

50

Minimum

Statistic

45

Maximum

Statistic

95

Mean

Statistic

63.45

Std. Deviation

Statistic

8.216

Variance

Statistic

67.507

Skewness

Statistic

.243

Std. Error

.055

Kurtosis

Statistic

-.401

Std. Error

.110

The normality test for the variable “Age in years” showed that the variable does not come from a normally distributed dataset (p < 0.001).

Table 3: Tests of Normality

Tests of Normality

 

Kolmogorov-Smirnova

Shapiro-Wilk

Statistic

df

Sig.

Statistic

df

Sig.

Age in years

.055

1995

.000

.989

1995

.000

a. Lilliefors Significance Correction

A boxplot was drawn to see the distribution of the dataset. A number of outliers were observed in the dataset further suggesting that the dataset is not symmetrical.

Figure 2: Boxplot for age in years

However, the histogram presented below suggests that the dataset seems to be normally distributed since the graph is almost symmetrical and in the shape of a bell-shaped curve.

Figure 3: Histogram for age in years

Question 3

Current research indicates that the number of everyday life stressors has risen in the last decade. Hospital records for 2014 show that 74% of Australians admitted to hospital for suspected myocardial infarction had normal blood pressure at the time of admission. The researchers have suggested, that due to increasing stress, the percentage of Australians admitted to hospital for suspected myocardial infarction who have normal blood pressure at the time of admission is now lower than this.

Conduct a Binomial Test using the ‘bp ’ variable to test the researchers’ hypothesis. Produce the relevant output and write a Binomial test report based on your output in the style presented in the course materials.

Solution

In this question, we conducted a Binomial test using the ‘bp’ variable to test the researchers’ hypothesis that 74% of Australians admitted to hospital for suspected myocardial infarction had normal blood pressure at the time of admission (Howell, 2007). The hypothesis set to be tested was;

Table 4: Descriptive Statistics

Descriptive Statistics

 

N

Mean

Std. Deviation

Minimum

Maximum

Blood pressure

1996

.79

.411

0

1

Table 5: Binomial Test

Binomial Test

 

Category

N

Observed Prop.

Test Prop.

Exact Sig. (1-tailed)

Blood pressure

Group 1

Normal

1568

.79

.74

.000

Group 2

Non-normal

428

.21

 

 

Total

 

1996

1.00

 

 

From table 5 above, we can clearly see that the proportion of Australians admitted to hospital for suspected myocardial infarction had normal blood pressure at the time of admission is 79% for the sample data provided. Binomial test that was conducted revealed that there is significant evidence that the proportion of Australians admitted to hospital for suspected myocardial infarction had normal blood pressure at the time of admission is greater than 74%. The claim by the researchers that the proportion is lower than 74% is therefore not significantly valid.

Question 4

Due to federal cuts to the Government Health System, the researchers predicted that the average length of stay in hospital for patients admitted for suspected myocardial infarction is now lower than the average of 5.5 days recorded in 2014.

Conduct a One-Sample t-test using the ‘los’ variable to test this prediction.

Produce the relevant output and write a One-sample t-test report based on your output in the style presented in the course materials.

Solution

The aim of this question was to test the claim that the average length of stay in hospital for patients admitted for suspected myocardial infarction is now lower than the average of 5.5 days recorded in 2014.

Hypothesis

Using one-sample t-test, we tested the above claim at 5% level of significance (John , 2006).

Table 6: One-Sample Statistics

 

 

N

Mean

Std. Deviation

Std. Error Mean

Length of stay

1995

5.54

1.439

.032

Table 7: One-Sample Test

 

 

Test Value = 5.5

t

df

Sig. (2-tailed)

Mean Difference

95% Confidence Interval of the Difference

Lower

Upper

Length of stay

1.112

1994

.266

.036

-.03

.10

The mean length of stay was found to be 5.54. Results from the one-sample t-test revealed that there is no evidence predicted that the average length of stay in hospital for patients admitted for suspected myocardial infarction is now lower than the average of 5.5 days recorded in 2014 (p > 0.05).

Question 5

The researchers have also claimed that the average length of stay in hospital for patients who have a history of diabetes is higher than the average for those who do not.

Conduct an Independent samples t-test using the ‘los’ and ‘diabetes’ variables to investigate this claim. Produce the relevant output and write an Independent samples t-test report based on your output in the style presented in the course materials.

Solution

In this question we tested the claim that the average length of stay in hospital for patients who have a history of diabetes is higher than the average for those who do not. The hypothesis is;

Where  is the average length of stay in hospital for patients who have a history of diabetes while  is the average length of stay in hospital for patients who do not have a history of diabetes.

To test this claim, independent t-test was conducted at 5% level of significance. Results are given the tables below.

Table 8: Group Statistics

Group Statistics

 

History of diabetes

N

Mean

Std. Deviation

Std. Error Mean

Length of stay

No

1780

5.52

1.374

.033

Yes

214

5.68

1.899

.130

Table 9: Independent Samples Test

 

Levene's Test for Equality of Variances

t-test for Equality of Means

F

Sig.

t

df

Sig. (2-tailed)

Mean Difference

Std. Error Difference

95% Confidence Interval of the Difference

Lower

Upper

Length of stay

Equal variances assumed

32.045

.000

-1.572

1992

.116

-.164

.104

-.368

.040

Equal variances not assumed

 

 

-1.223

240.51

.223

-.164

.134

-.427

.100

An independent samples t-test was performed to compare the average length of stay in hospital for patients who have a history of diabetes is higher than the average for those who do not (Zimmerman, 2007). There was no significant difference in the length of stay for the two groups of patients. The length of stay for those with history of diabetes (M = 5.68, SD = 1.90, N = 214) was not significantly different to those with no history of diabetes (M = 5.52, SD = 1.37, N = 1780), t(1992) = -1.57, p > .001, one-tailed.

References

Howell, D. C. (2007). Statistical methods for psychology.

John , R. A. (2006). Mathematical Statistics and Data Analysis.

Zimmerman, D. W. (2007). A Note on Interpretation of the Paired-Samples t Test. Journal of Educational and Behavioral Statistics, 22(3), 349–360.

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