Question

An article found that Massachusetts residents spent an average of $857. 50 on the lottery in 2021, more than three times the U. S. Average. A researcher at a Boston think tank believes that Massachusetts residents spend less than this amount annually. She surveys 100 Massachusetts residents and asks them about their annual expenditures on the lottery.

a. Specify the competing hypotheses to test the researcher’s claim.


multiple choice 1


H0: μ ≥ 857. 50; HA: μ < 857. 50


H0: μ = 857. 50; HA: μ ≠ 857. 50


H0: μ ≤ 857. 50; HA: μ > 857. 50


b-1. Calculate the value of the test statistic. (Round to four decimal places. )


b-2. Find the p-value. (Round to four decimal places. )


c. At α = 0. 05, what is the conclusion?


multiple choice 2


Do not reject H0; there is insufficient evidence to state that the average Massachusetts resident spends less than $857. 50 on the lottery annually


Reject H0; there is insufficient evidence to state that the average Massachusetts resident spends less than $857. 50 on the lottery annually


Do not reject H0; there is sufficient evidence to state that the average Massachusetts resident spends less than $857. 50 on the lottery annually


Reject H0; there is sufficient evidence to state that the average Massachusetts resident spends less than $857. 50 on the lottery annually

Answer 1

Cannot be determined

Explanation:

a. The hypotheses are:

H0: μ ≥ 857.50 (null hypothesis) HA: μ < 857.50 (alternative hypothesis)

b-1. We need more information to calculate the test statistic.

b-2. We need more information to calculate the p-value.

c. To determine the conclusion, we need to compare the p-value to the level of significance (α).

If the p-value is less than α (0.05), we reject the null hypothesis (H0). If the p-value is greater than or equal to α (0.05), we fail to reject the null hypothesis (H0).

We do not have the p-value to compare with α yet, so we cannot make a conclusion.

Therefore, the answer to multiple choice 1 is H0: μ ≥ 857.50; HA: μ < 857.50, and the answer to multiple choice 2 is cannot be determined yet.