Question

Sample A

Answer 1

a) Suppose the weight loss for sample A be denoted by Xa and the population mean of the weight loss corresponding to sample A be Ma. Then, we want to test

H0: Ma = -5 vs H1: Ma>-5

           One-Sample Test
           Test Value = -5
95% Confidence Interval of the Difference
t df   Sig. (2-tailed)   Mean Difference Lower Upper
SampleA   1.679   29   .104 1.86667 -.4073 4.1406

Since, the p-value is 0.104 which is greater than 0.05, the null hypothesis can not be rejected at 5% level of significance. Hence, mean weight loss is not -5.

b) Here also the hypothesis is the same as above. The result is given below:

           One-Sample Test
           Test Value = -5
95% Confidence Interval of the Difference
t df   Sig. (2-tailed)   Mean Difference Lower Upper
SampleC   -2.280   29   .030 -6.33333 -12.0152 -.6514

Since, the p-value is 0.03 which is less than 0.05, so the null hypothesis is rejected at 5% level of significance and we can conclude that the average weight loss is significant.

c) The difference of sample mean (weight loss) and proposed value (-5) is 1.8667 for sample A, whereas it is -6.3333 for sample C. 95% confidence interval for sample A does not contain the point -5, both the lower and upper confidence limits are greater than -5. So, the test is insignificant for sample A.

For sample C, the 95% CI does not contain the point -5, and also both the upper and lower confidence limits are smaller than -5. Hence, in this case, the test is significant.