Math 1530 Chapter 7 Review Questions
1. Write the null and alternative hypotheses for the following: A cereal company claims that the
mean weight of the cereal in its packets is at least 14 oz.
2a. Assume that the data has a normal distribution and sigma (σ) is not known. The sample size is
18. Find the critical t value for:
2a. Right tail test, α = 0.1. (Hint: Use Table A-3)
2b. Left tail test, α = 0.05.
2c. Two tailed test, α = 0.01
3. Find the test statistic for the following situations:
a. The claim is that the mean is 0.21; the sample statistics include: n = 32; x-bar = 0.83, s = 0.24.
b. The claim is that the mean < 1.39; sample stats include: n = 87; x-bar = 0.83; s = 0.16.
c. The claim is that the mean is at least 50; sample stats include: n = 100; x-bar = 54.8; s = 3.6
4. An entomologist writes an article in a scientific journal which claims that fewer than 7 in 10,000
(0.0007) male fireflies are unable to produce light due to a genetic mutation. Assuming that a
hypothesis test of the claim has been conducted and that the conclusion is to REJECT the null
hypothesis, state the conclusion in non-technical terms.
A. There is sufficient evidence to support the claim that the true proportion is greater than
.0007
B. There is not sufficient evidence to support the claim that the true proportion is less than
.0007
C. There is not sufficient evidence to support the claim that the true proportion is greater than
.0007
D. There is sufficient evidence to support the claim that the true proportion is less than .0007.
5. Suppose you wish to use a hypothesis test to test a claim made by a juice bottling company
regarding the mean amount of juice in its 16 oz bottles. Why does the original claim sometimes
become the null hypothesis, and why does it sometimes become the alternative hypothesis. Give
examples.
7. A store manager claims that the mean amount of time customers spend waiting in line is less
than 3.7 minutes. You wish to test this claim at the 0.05 level of significance. The mean waiting
time for a random sample of n = 85 customers is 3.3 minutes with a sd of 0.8 minutes. Compute the
value of the test statistic.
8. The National Weather Service says that the mean daily high temperature for October in a large
Midwestern city is 56° F. A local weather service wants to test the claim of 56° because it believes
it is lower. A sample of mean daily high temps for October over the past 31 years yields x-bar = 54
with s = 5.6. Test the NWS claim using the “Classical Method” at the .05 sig. level.
