Question

A random sample of n₁ = 297 voters registered in the state of California showed that 144 voted in the last general election. A random sample of n₂ = 216 registered voters in the state of Colorado showed that 130 voted in the most recent general election. Do these data indicate that the population proportion of voter turnout in Colorado is higher than that in California? Use a 5% level of significance.

(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. (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 = 0.05 level, we fail to 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 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.

Reject the null hypothesis, there is insufficient evidence that the proportion of voter turnout in Colorado is greater than that in California.

Reject the null hypothesis, there is sufficient evidence that the proportion of voter turnout in Colorado is greater than that in California.

     Fail to reject the null hypothesis, there is sufficient evidence that the proportion of voter turnout in Colorado is greater than that in California.

Fail to reject the null hypothesis, there is insufficient evidence that the proportion of voter turnout in Colorado is greater than that in California.

Answer 1

Now , the estimate of the sample proportions are ,

The pooled estimate is ,

(a) The level of significace is ,

The null and alternative hypothesis is ,

The test is left-tailed test.

(b) The standard normal. We assume the population distributions are approximately normal.

The test statistic is ,

(c) The p-value is ,

p-value= ; The Excel function is , =1-NORMDIST(2.62,0,1,TRUE)

(d) Decision : Here , p-value<0.05

Therefore , reject Ho.

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

(e) Conclusion :

Reject the null hypothesis, there is sufficient evidence that the proportion of voter turnout in Colorado is greater than that in California.