Question

A poll of 1350 adults in the United States asked how much confidence they had in banks. A total of 203 adults said 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. Can you conclude that the economist's claim is true? Use the α = 0.01 level of significance.

Fill in the blanks

State the null and alternative hypothesis

Ho:

H1:

The test statistics is . Round your answer in 4 decimal places

The critical value is . Round your answer in 2 decimal places

The P-value is . Round your answer in 2 decimal places.

Decision

A) Reject the Ho

B) Do not reject the Ho

Type A or B in the box

Conclusion:

A) We conclude that the economist's claim is true that is less than 15% of U.S. adults have a great deal of confidence in banks.

B) We can not conclude that the economist's claim is true that is less than 15% of U.S. adults have a great deal of confidence in banks.

Type A or B in the box

Answer 1

Step 1:

Ho: p = 0.15

Ha: p < 0.15 (Claim)

Null hypothesis states that the proportion of US adults who have great deal of confidence in banks is equal to 0.15

Alternative hypothesis states that the proportion of US adults who have great deal of confidence in banks is less than 0.15

Step 2: test statistics

z stat = 0.0381

Step 3: Critical value

z critical for left tailed test at = 0.01 is - 2.33

p value: P(z < 0.0381) = 0.516

Step 4: Decision

As z stat does not fall in the rejection area, we fail to reject the Null hypothesis.

Also as the p value (0.516) is greater than 0.01, we fail to reject the Null hypothesis.

Step 5 : Conclusion

B) We can not conclude that the economist's claim is true that is less than 15% of U.S. adults have a great deal of confidence in banks.