confidence in banks

Question

Confidence in banks: A poll conducted by the General Social Survey asked a random sample of 1325 adults in the United States how much confidence they had in banks and other financial institutions. A total of 149 adults said that they had a great deal of confidence. An economist claims that less than 15% of U.S. adults have a great deal of confidence in banks.

a.	State the appropriate null and alternate hypotheses.
b.	Compute the test statistic z.
c.	Using α = 0.05, can you conclude that the executive’s claim is true?
d.	Using α = 0.01, can you conclude that the executive’s claim is true?

Answer 1

The null hypothesis is p=0.15

The alternative hypothesis is p<0.15

The test statistic is -3.827. This can be calculated using a 1-PropZTest.

The p-value for the problem is 0.00006.

At both the 0.01 and 0.05 level, there is sufficient evidence to support the claim that less than 15% of US adults have a great deal of confidence in banks. This can be determined using the p-value:

If p<α then reject the null

If p>α then fail to reject the null

It can also be determined using the test statistic.

If the test statistic for a left-tailed test is less than the z score for each given α then then null hypothesis is rejected

If the test statistic for a left tailed test is greater than the z score for each given α then fail to reject the null hypothesis.