Question

A poll conducted in 2012 asked a random sample of 1358 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 13% of U.S. adults have a great deal of confidence in banks. Can you conclude that the economist's claim is true? Use both α=0.10 and α=0.01 levels of significance and the P-value method with the TI-84 Plus calculator.

a. state null and alternative hypothesis. what tail is the hypothesis test?

b. Compute the value of the test statistic.

c. Using α=0.10, can you conclude that greater than 71% of emails are spam?

d. Using α=0.01, can you conclude that greater than 71% of emails are spam?

e. state conclusion

Answer 1

From Ti 83 Plus calculator

a) Null hypothesis: H0: p0 = 0.13

Alternative hypothesis H1: p0 < 0.13

b) Test statistic Z= -2.222

c) From the output p-value = 0.0131

At level of significance 0.10, p-value is less than 0.10, we reject null hypothesis and conclude that less than 13% of US adults have a great deal of confidence

At level of significance 0.01, p-value is greater than 0.01, we accept null hypothesis and conclude that Not less than 13% of US adults have a great deal of confidence