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# Hypothesis Testing for a Single Mean: Fat Content of Hamburgers

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1. 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 statistic.
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. Please be sure to show some work.
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?

2. 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.

3. Should the results from hypothesis tests always agree with the confidence interval at the same confidence level? Why or why not?

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#### Solution Preview

Please see the attached Word document for solutions/explanations.

In this problem set you will get some practice working with data and performing hypothesis tests. Similar questions will be on your test next week.
Good luck and enjoy!

1. 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 statistic.

The sum of the observations is:

The sum of the squares of the 40 observations is:

The mean of the sample is:

The standard deviation of the sample is:

b. In order to perform this hypothesis test, what assumption(s) must be met?

For this hypothesis test the sample size of is large (Samples are considered to be large if the sample size is greater than 30). The central limit theorem tells us that for large samples, the sampling distribution of the sample mean follows an approximately normal distribution regardless of the shape of the population ...

#### Solution Summary

The solution discusses the fat content of hamburgers in the hypothesis testing for a single mean.

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