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 = 88urban residents showed that r₁ = 13 subscribed, and a random sample of n₂ = 99 suburban residents showed that r₂ = 20 subscribed. Does this indicate that a higher proportion of suburban residents subscribe to Sporting News? Use a 5% level of significance.

What are we testing in this problem?

difference of means
paired difference    

single proportion

single meandifference of proportions

(a) What is the level of significance?


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

(b) 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 Student's t. The number of trials is sufficiently large.

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

What is the value of the sample test statistic? (Test the difference p₁ − p₂. Do not use rounded values. Round your final answer to two decimal places.)


(c) Find (or 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

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

(d) Based on your answers in parts (a) to (c), 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.

(e) 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

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

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