Confidence in banks

(14.)        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.

H₀: The proportion of individuals with a great deal of confidence in banks is less than 15% i.e., p < 0.15

H₁: The proportion of individuals with a great deal of confidence in banks is greater than or equal to 15% i.e., p ≥ 0.15

b.       Compute the test statistic z.

p̂ = 1491325=0.112

standard deviation = 0.15(1-0.15)1325

 = 0.00981

              Z = 0.112-0.150.00981

                             = -3.87

c.        Using α = 0.05, can you conclude that the executive’s claim is true?

At α = 0.05, the critical value is -1.645. Since the statistic value is less than the critical value, we reject the null hypothesis and conclude that the executive’s claim is not true at a 95% confidence level.