STAT 350 Confidence Interval & Statistical Decision Questions

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Homework #8: Chapters 10.1-10.3, Due 11/22/22 by Midnight PT
Question 1:
Assume that 30% of students at a university wear contact lenses. A random sample of 100 students is
selected.
a.
Describe the sampling distribution of the sample proportion of students who wear contacts.
b. What is the probability that at most one third of this sample wear contacts?
Question 2:
In a survey conducted by Andrew Callaghan, 130 of the 250 people that were randomly surveyed
support student loan forgiveness.
a. Construct a 90% confidence interval to estimate the true population proportion of people that
support student loan forgiveness.
b. Interpret the confidence interval from part (a).
Question 3:
A humane society claims that 30% of U.S. households own a dog. In a random sample of 210 U.S.
households, 80 say they own a dog. Is there enough evidence to show this percent has changed? Use a
level of significance of 0.05.
a. State the null and alternative hypotheses.
b. Calculate the test statistic
c. Find the critical value for the rejection region or find the p-value of the test statistic.
d. Make a statistical decision.
e. State your conclusion in context of the problem.
Question 4:
[Assume all assumptions and conditions are satisfied for Question 4]
Question 5:
[For part (b), perform the 5-step process of the appropriate test]

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