Question

In a recent year, a poll asked 2157 random adult citizens of a large country how they rated economic conditions. In the poll, 36% rated the economy as Excellent/Good. A recent media outlet claimed that percentage of citizens who felt the economy was in Excellent/Good shape was 34%. Does the poll support this claim?

a) Let p be the proportion of adult citizens who felt the economy was in Excellent/Good shape. What are the null and alternative hypotheses for the test?

b) Which of the following conditions are satisfied? Select All that apply.

- There are more than 10 ''successes'' and 10 ''failures''

-The data are independent

-The sample is random

-Less than 10% of population was sampled

c) Test the claim at 1% level of significance. State your conclusion.

d) Find the p-value

e) Find a 99% confidence interval for the proportion of adults who rated the economy as Excellent/ Good.

f) Does your confidence interval provide evidence to support the conclusion from the hypothesis test?

Answer 1

a) The following null and alternative hypotheses need to be tested:

b)

- There are more than 10 ''successes'' and 10 ''failures''

-The data are independent

-The sample is random

c) The rejection region for this two-tailed test is

The z-statistic is computed as follows:

Since it is observed that |z| = 1.9608 < zc = 2.58, it is then concluded that the null hypothesis is not rejected.

d) The P-value is p=P(|Z|>1.9608)=2*P(Z<1.9608)=2*0.025=0.05

d) The 99% confidence interval for p is: 0.33 < p < 0.39.

f) Since the onfidence interval contains the population proportion 0.34 , hence the null hypothesis is not rejected.