Confidence in banks: A poll conducted asked a random sample of 1239 adults in the United States how much confidence they had in banks and other financial institutions. A total of 158 adults said that they had a great deal of confidence. An economist claims that greater than 11% of U.S. adults have a great deal of confidence in banks. Can you conclude that the economist's claim is true? Use both =α0.10 and =α0.01 levels of significance and the P-value method with the TI-84 Plus calculator.Part 1 of 5(a) State the appropriate null and alternate hypotheses.:H0 <p0.11:H1 >p0.11This hypothesis test is a ▼right-tailed test.Correct Answer:=:H0p0.11>:H1p0.11This hypothesis test is a right-tailed test.Part: 1 / 51 of 5 Parts CompletePart 2 of 5(b) Compute the value of the test statistic. Round the answer to at least two decimal places.=z
Question
Confidence in banks: A poll conducted asked a random sample of 1239 adults in the United States how much confidence they had in banks and other financial institutions. A total of 158 adults said that they had a great deal of confidence. An economist claims that greater than 11% of U.S. adults have a great deal of confidence in banks. Can you conclude that the economist's claim is true? Use both =α0.10 and =α0.01 levels of significance and the P-value method with the TI-84 Plus calculator.Part 1 of 5(a) State the appropriate null and alternate hypotheses.:H0 <p0.11:H1 >p0.11This hypothesis test is a ▼right-tailed test.Correct Answer:=:H0p0.11>:H1p0.11This hypothesis test is a right-tailed test.Part: 1 / 51 of 5 Parts CompletePart 2 of 5(b) Compute the value of the test statistic. Round the answer to at least two decimal places.=z
Solution
The null hypothesis (H0) and the alternate hypothesis (H1) are as follows:
H0: p = 0.11 (The proportion of U.S. adults who have a great deal of confidence in banks is 11%) H1: p > 0.11 (The proportion of U.S. adults who have a great deal of confidence in banks is greater than 11%)
This is a right-tailed test because we are testing if the proportion is greater than a certain value.
Next, we need to compute the value of the test statistic. The formula for the test statistic in a proportion hypothesis test is:
z = (p̂ - p0) / sqrt[(p0 * (1 - p0)) / n]
where p̂ is the sample proportion, p0 is the proportion in the null hypothesis, and n is the sample size.
In this case, p̂ = 158 / 1239 = 0.1275, p0 = 0.11, and n = 1239.
Substituting these values into the formula gives:
z = (0.1275 - 0.11) / sqrt[(0.11 * (1 - 0.11)) / 1239]
Calculating this will give the value of the test statistic.
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