Question

A study is made of residents in Phoenix and its suburbs concerning the proportion of residents who subscribe to Sporting News. A random sample of n1 = 88 urban residents showed that 10 subscribed, and a random sample of n2 = 99 suburban residents showed that 19 subscribed. Does this indicate that a higher proportion of suburban residents subscribe to Sporting News? Use a 5% level of significance.

a.)What are we testing in this problem?

-difference of proportions

-single mean

-paired difference

-single proportion

-difference of means

b.) What is the level of significance? _____

c.) State the null and alternate hypotheses.

-H0: p1 = p2; H1: p1 ≠ p2

-H0: p1 > p2; H1: p1 ≤ p2

-H0: p1 ≤ p2; H1: p1 > p2

-H0: p1 ≠ p2; H1: p1 = p2

-H0: p1 < p2; H1: p1 ≥ p2

-H0: p1 ≥ p2; H1: p1 < p2

d.) What sampling distribution will you use? What assumptions are you making?

-The Student's t. We assume the population distributions are approximately normal.

-The standard normal. The number of trials is sufficiently large.

-The standard normal. We assume the population distributions are approximately normal.

-The Student's t. The number of trials is sufficiently large.

e.) What is the value of the sample test statistic? (Test the difference p1 − p2). Round your answer to two decimal places.______--

f.) Estimate the P-value.

-P-value > 0.250

-0.125 < P-value < 0.250

-0.050 < P-value < 0.125

-0.025 < P-value < 0.050

-0.005 < P-value < 0.025

-P-value < 0.005

g.) Sketch the sampling distribution and show the area corresponding to the P-value.

h.) Will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

-At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.

-At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.

-At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

-At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

I.) Interpret your conclusion in the context of the application.

-There is sufficient evidence at the 0.05 level to conclude that the proportion of suburban residents subscribing to Sporting News is higher.

-There is insufficient evidence at the 0.05 level to conclude that the proportion of suburban residents subscribing to Sporting News is higher.

Answer 1