Question

In 2016, it was reported that 80 of 500 Utah families had incomes below the poverty level. At the same time, 54 of 450 Wyoming families had incomes below the poverty level. You need to find out if there was a significant difference in proportion of families with incomes below the poverty level in these two states.

(a) State the research question.

(b) State both the null and alternative hypotheses.

(c) Determine the critical values (use 5% significance level).

(d) Calculate the standard error (see page 160 in the Pineapple Book).

(e) Calculate the test statistic, and state the decision regarding the null hypothesis.

(f) Calculate the p-value for the test.

(g) Assess the strength of your decision in part (d) using the p-value.

(h) Calculate a 95% confidence interval for the difference between the two corresponding population proportions (see pages 280-281 in the Blue Book).

(i) Which state has a higher proportion of families with incomes below the poverty level, and by how much? Be specific.

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Answer 1