Reference no: EM132410305
A dietician is out shopping one day for healthy snacks for the children she supervises each day. She spots one on the shelf that is of interest to her and reminds her of a similar product she recently saw advertised on tv. It claims to have an average of 20 calories per bar, a number that seems too high to her as she looks carefully at the ingredients of the product. Having just finished a statistics course at UIW, this dietician uses the opportunity to perform an important hypothesis test. She does a bit of research online and finds the standard deviation for the whole population of bars is approximately equal to 7 calories. Then she sends a random sample of 49 bars to a friend of hers who has a lab where the calories contained in each of the 49 bars can be precisely measured. Once tested, the average number of calories for this sample of 49 bars turns out to be (only) 18 calories! She smiles...and then decides to continue on with the hypothesis test.
a. Why does she smile EVEN BEFORE she has done any computations?
b. Should the dietician use t or z to perform this test? Why so?
c. What are the null and alternate hypotheses required for this test?
d. Compute the test statistic for this test. Be sure to show your work in the space provided below.
e. What is the p-value associated with this test statistic?
f. At a 95% level of confidence with alpha set to 0.05 (5%), should she reject the null hypothesis? Why or why not?
g. At a 99% level of confidence with alpha set to 0.01 (1%), should she reject the null hypothesis? Why or why not?