Question

a. The standard deviation of a sample of data was 14. Find the variance.

B. Given the sample data 5, 0, 7, 5, 9, and 6, find its range

C.

A new​ weight-loss program claims that participants will lose an average of more than 10 pounds after completing it. The data table shows the weights of five individuals before and after the program.

	1	2	3	4	5
weight before	264	220	285	264	195
weight after	240	223	267	250	175

We need to test the hypothesis that the population mean of differences exceed 10.  That is,

H0:  

H1:   .  

Use 5% level of significance.

Find the test statistic.

(Provide two  significant digits to the right of the decimal point)

C.

A person can take either of two routes to work, through Matteson or Richton Park. Both take on average 35 minutes, and travel times are Normally distributed. But are the variances of the travel times different? A random sample with n = 8 using the Matteson route, and another random sample with n = 6 using the Richton Park route, showed a variance of 45 (units: square minutes) and 30 respectively. To test whether the variances are different, the following test of hypothesis should be done:

H0:

H1:  

What is the value of the test statistic?

Answer 1

We calculate the variance and the range using the formula mentioned.For the first hypothesis test problem, we mention the null and alternate hypothesis and calculate the test statistic using the formula mentioned. The p value is obtained from STATKEY (image attached for reference). We compare the p value and alpha and make the required decision. For the second hypothesis test problem, the test statistic is calculated using the formula mentioned. The critical value is obtained from STATKEY(image attached). We compare the test statistic with the critical value and make the required decision.