## Statistical Inference QUESTION 1
1. The first several questions will not be related to your analysis of the R data set for this week, and will involve hand calculation of confidence intervals and hypothesis tests.
Suppose that someone has provided you with the following numerical summary from R Commander of the systolic blood pressure (SBP) of a group of 60 individuals:
mean sd IQR 0% 25% 50% 75% 100% n
119.6 12.9 14.25 87 114.75 119 129 154 60
For inference about mean SBP in the population from which this sample came, enter the point estimate.
1 points
QUESTION 2
1. Refer to problem 1. Calculate the standard error that will be used to calculate the confidence interval and hypothesis test statistic for mean SBP. Round to 2 decimal places.
1 points
QUESTION 3
1. Refer to problem 1. Determine the quantile from the t distribution that will be used to build a 95% confidence interval for mean SBP in the population. Round to 2 decimal places. (Hint: You ill have need of R’s qt() function).
1 points
QUESTION 4
1. Refer to problem 1. Enter the 95% confidence interval for mean SBP in the population. Your answer should be in interval notation – (lower limit, upper limit) – with limits rounded to 1 decimal place. (Hint: Use the heuristic formula Point Estimate +/- Quantile*Standard Error from this week’s lectures.)
1 points
QUESTION 5
1. Refer to problem 1. Suppose we are testing the null hypothesis that the mean SBP in the population is equal to 115, i.e. H0: µ = 115. Calculate the test statistic that will be used to evaluate this hypothesis. Roud to 2 decimal place. (Hint: Use the heuristic formula (Point Estimate – Null Value)/Standard Error).
1 points
QUESTION 6
1. Refer to problem 1. Calculate the p-value for testing the null hypothesis that the mean SBP in the population is equal to 115, i.e. H0: µ = 115. Round to 4 decimal places (since you should get a small number). (Hint: You will have need of the pt() function in R).
1 points
QUESTION 7
1. Using a significance level of 0.05 for the hypothesis test, what is the correct decision about the null hypothesis?
Accept H0
Reject H0
1 points
QUESTION 8
1. Here are 3 free points – the answer to this question is TRUE.
Here are some problem for which you can practice calculating confidence intervals and hypothesis tests. Based on the information given, you should be able to calculate the confidence intervals and p-values. If you have any trouble, get in touch with your instructor.
1. Sample mean = 15.4, Sample SD = 2.7, N = 45.
1. The 95% confidence interval for the mean is (14.6, 16.2). The p-value for a test of the null hypothesis H0: µ = 15.5 is 0.80
2. Sample mean = 58, Sample SD = 16, N = 72.
1. The 95% confidence interval for the mean is (54.2, 61.8). The p-value for a test of the null hypothesis H0: µ = 55 is 0.12
3. Sample mean = 2.45, Sample SD = 0.98, N = 37.
1. The 95% confidence interval for the mean is (2.12, 2.78). The p-value for a test of the null hypothesis H0: µ = 2 is 0.0083
4. Sample mean = 130, Sample SD = 15, N = 84.
1. The 95% confidence interval for the mean is (126.7, 133.3). The p-value for a test of the null hypothesis H0: µ = 135 is 0.0030

– True
– False
3 points
QUESTION 9
1. This and all remaining questions refer to your analysis of the EmployeeSurvey.Rdata data set.
Enter the 95% confidence interval for the mean score on the Advancement item of the survey. Round to 2 decimal places. Your answer should look something like “(2.12, 4.35)” (these numbers are made up).
1 points
QUESTION 10
1. Enter the 95% confidence interval for the mean score on the Benefits item of the survey. Round to 2 decimal places.
1 points
QUESTION 11
1. Enter the 95% confidence interval for the mean score on the Compensation item of the survey. Round to 2 decimal places.
1 points
QUESTION 12
1. Enter the 95% confidence interval for the mean score on the Environment item of the survey. Round to 2 decimal places.
1 points
QUESTION 13
1. Enter the 95% confidence interval for the mean score on the Social item of the survey. Round to 2 decimal places.
1 points
QUESTION 14
1. At a significance level of 0.05, what decision is made about the null hypothesis that the mean score on the Advancement item of the survey was 5, H0: µ = 5?
Accept H0
Reject H0
1 points
QUESTION 15
1. At a signfiicance level of 0.05, what decision is made about the null hypothesis that the mean score on the Benefits item of the survey was 5, H0: µ = 5?
Accept H0
Reject H0
1 points
QUESTION 16
1. At a significance level of 0.05, what decision is made about the null hypothesis that the mean score on the Compensation item of the survey was 5, H0: µ = 5?
Accept H0
Reject H0
1 points
QUESTION 17
1. At a significance level of 0.05, what decision is made about the null hypothesis that the mean score on the Enviornment item of the survey was 5, H0: µ = 5?
Accept H0
Reject H0
1 points
QUESTION 18
1. At a significance level of 0.05, what decision is made about the null hypothesis that the mean score on the Social item of the survey was 5, H0: µ = 5?
Accept H0
Reject H0
1 points
QUESTION 19
1. Recall that a mean score of 5 is an important threshold for the items on the survey – scores below 5 indicate a deficiency in the workplace at the company and scores above 5 indicate sufficiency in the workplace.
Based on this, and the results of your anlayses, what is an appropriate qualitative judgment about Advancement opportunities at the company (refer to your analysis of the variable adv)?
The company is deficient in offering advancement opportunities
The company is sufficient in offering advancement opportunities
1 points
QUESTION 20
1. Based on the results of your anlayses, what is an appropriate qualitative judgment about Benefits at the company (refer to your analysis of the variable ben)?

– The company is deficient in benefits offerings
– The company is sufficient in benefits offerings
1 points
QUESTION 21
1. Based on the results of your anlayses, what is an appropriate qualitative judgment about Compensation at the company (refer to your analysis of the variable comp)?

The company offers deficient compensation
The company offers sufficient compensation
1 points
QUESTION 22
1. Based on the results of your anlayses, what is an appropriate qualitative judgment about the Environment at the company (refer to your analysis of the variable env)?

The physical work environment is deficient
The physical work environment is sufficient
1 points
QUESTION 23
1. Based on the results of your anlayses, what is an appropriate qualitative judgment about the Social culture at the company (refer to your analysis of the variable soc)?

The social culture is deficient 