The Professor's Response
3. A cable company in Tallahassee claims that at least 90 percent of customers are very satisfied with the service they receive. To test this claim, the local newspaper surveyed 150 customers, using simple random sampling. Among the sampled customers, 132 reported they are very satisfied. Based on these findings, is the cable company's claim valid? Use a 0.05 level of significance.
[Hint: Conduct a Test of Hypothesis for a Sample Proportion] (5 points)
I NEED HELP
See the professor's answer below.
Hi Andrea,
The claim is p ≥ 0.90
Ho: p ≥ 0.90
Ha: p < 0.90
Data:
n = 150
x = 132
p-hat = x/n = 0.88
alpha = 0.05
Test Stat: z = (0.88 - 0.90)/SqrRoot(0.90*0.10/150) = - 0.82
Critical value and rejection region: look up 0.05 in one-tail on the t-table in the last row to get z = -1.645 Reject if the test stat is less than -1.645.
Since the test stats is not less than -1.645, do not reject the null hypothesis, do not support the alternative hypothesis.
Conclusion: The sample data does not allow rejection of the claim that at least 90 percent of the customers are very satisfied.
Hope that helps,
Professor McGuckian