An organization published an article stating that in any one-year period, approximately11.5percent of adults in a country suffer from depression or a depressive illness. Suppose that in a survey of100 peoplein a certain town,nineof them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult population in the country.

A)Is this a test of one mean or proportion?

B)State the null and alternative hypotheses.

C)Is this a right-tailed, left-tailed, or two-tailed test?

D)What symbol represents the random variable for this test?

_x

n

P'

x

E)In words, define the random variable for this test.

-the proportion of people in the town surveyed not suffering from depression or a depressive illness

-the number of people in the town surveyed not suffering from depression or a depressive illness

-the number of people in the town surveyed suffering from depression or a depressive illness

the number of people in the survey

-the proportion of people in the town surveyed suffering from depression or a depressive illness

F)Calculate the following.

(i) Enter your answer as a whole number.

x=

(ii) Enter your answer as a whole number.

n=

(iii) Enter your answer to two decimal places.

p'=

G)Calculate_x. (Round your answer to three decimal places.)

Show the formula set-up.

H)State the distribution to use for the hypothesis test.

I)Find thep-value. (Round your answer to four decimal places.)

J)At a pre-conceived= 0.05, what are your following?

(i) Decision:

• Do not reject the null hypothesis.
• Do not reject the alternative hypothesis.
• Reject the alternative hypothesis.
• Reject the null hypothesis

(ii) Reason for the decision:

• p-value <
• p-value =
• p-value =/2
• p-value >
• p-value >/2

(iii) Conclusion:

• At the 5% level of significance, there is sufficient evidence to conclude that the proportion of people in the town with depression or depressive illness is higher than 0.115.
• At the 5% level of significance, there is insufficient evidence to conclude that the proportion of people in the town with depression or depressive illness is lower than 0.115.
• At the 5% level of significance, there is insufficient evidence to conclude that the proportion of people in the town with depression or depressive illness is lower than 0.885.
• At the 5% level of significance, there is sufficient evidence to conclude that the proportion of people in the town with depression or depressive illness is equal to 0.115.
• At the 5% level of significance, there is insufficient evidence to conclude that the proportion of people in the town with depression or depressive illness is higher than 0.885.