Discuss the below:
Q1. The fat content was determined for 40 hamburgers sold by a fast food restaurant. The results in grams appear below.
20.0 18.7 21.6 20.9 21.8 20.2 19.7 18.9 19.5 21.5
19.3 21.2 18.4 21.0 21.6 20.6 20.7 21.9 20.1 17.1
18.1 21.1 19.3 21.5 20.1 16.5 18.9 17.4 20.8 18.5
21.6 23.1 20.5 22.0 20.6 17.5 16.1 20.1 21.8 19.4
a. Find the sample mean and standard deviation for this data set. Put these values in the space below. Please be sure to label which value is which statistics
b. In order to perform this hypothesis test, what assumption(s) must be met?
c. Are the assumption(s) met? Please provide evidence if necessary. If you create a plot, please make sure to include it below or attach it to the back of this packet.
d. The fast food restaurant claims that their hamburgers have 19.35 grams of fat or less. A consumer group claims that in fact, their fat content is more than 19.35 grams. What are the null and alternate hypotheses for this test? Why?
e. Calculate the test statistic or the p-value.
f. What is the critical value for this hypothesis test using the significance level associated with a 90% confidence interval?
g. State the decision for this test.
h. What conclusions can you draw about the fat content of the hamburgers?
Q2. Using the fat content data above, do the following.
a. Create a 90% confidence interval. Please be sure to show your work
b. Interpret this interval.
c. Does this interval agree with your conclusions from number 1 above? Explain/support your answer.
Q3. Should the results from hypothesis tests always agree with the confidence interval at the same confidence level? Why or why not?