Question

Confidence in banks: A poll conducted in 2012 asked a random sample of 1342 adults in the United States how much confidence they had in banks and other financial institutions. A total of 143 adults said that they had a great deal of confidence. An economist claims that less than14% 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.

(b) Compute the P-value. Round the answer to at least four decimal places.

P-value= ___

Answer 1

Solution:

Given:

n = sample size = 1342

x = Number of adults said that they had a great deal of confidence = 143

Claim:  less than 14% of U.S. adults have a great deal of confidence in banks.

that is: p < 0.14

levels of significance:

α = 0.10 and α = 0.01

Thus hypothesis are:

H0: p = 0.14 Vs H1: p < 0.14

Use following step in TI 84 to find P-value:

Press STAT and select 1-PropZTest

Enter numbers:

Click on calculate and press Enter

P-value = 2.0725672E-4

Since this is scientific number with negative power of 4

thus we need to move 4 decimal places to left side

thus

P-value = 0.00020725672

P-value = 0.0002

Decision Rule at α = 0.10:
Reject null hypothesis H0, if P-value < 0.10 level of significance, otherwise we fail to reject H0

Decision Rule at α = 0.01:
Reject null hypothesis H0, if P-value < 0.01 level of significance, otherwise we fail to reject H0

Since P-value = 0.0002 is less than both level of significance 0.10 and 0.01, we reject null hypothesis H0.

Conclusion:
At both level of significance 0.10 and 0.01, there is sufficient evidence to support an economist claims that less than1 4% of U.S. adults have a great deal of confidence in banks.