Question

A random sample of n₁ = 150 people ages 16 to 19 were taken from the island of Oahu, Hawaii, and 14 were found to be high school dropouts. Another random sample of n₂ = 137people ages 16 to 19 were taken from Sweetwater County, Wyoming, and 5 were found to be high school dropouts. Do these data indicate that the population proportion of high school dropouts on Oahu is different (either way) from that of Sweetwater County? Use a 1% level of significance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: p₁ = p₂; H₁: p₁ < p₂H₀: p₁ = p₂; H₁: p₁ ≠ p₂     H₀: p₁ ≠ p₂; H₁: p₁ = p₂H₀: p₁ = p₂; H₁: p₁ > p₂

(b) What sampling distribution will you use? What assumptions are you making?

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.The Student's t. 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. (Round your answer to four decimal places.)


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 = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.     At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.01 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.

Reject the null hypothesis, there is sufficient evidence that the proportion of high-school dropouts on Oahu differs from that of Sweetwater County.Fail to reject the null hypothesis, there is insufficient evidence that the proportion of high-school dropouts on Oahu differs from that of Sweetwater County.     Fail to reject the null hypothesis, there is sufficient evidence that the proportion of high-school dropouts on Oahu differs from that of Sweetwater County.Reject the null hypothesis, there is insufficient evidence that the proportion of high-school dropouts on Oahu differs from that of Sweetwater County.

Answer 1