Question

A presidential candidate's aide estimates that, among all college students, the proportion who intend to vote in the upcoming election is at most 75% . If 209 out of a random sample of 275 college students expressed an intent to vote, can the aide's estimate be rejected at 0.1 the level of significance? Perform a one-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) The null hypothesis: The alternative hypothesis: The type of test statistic: The value of the test statistic: (Round to at least three decimal places.) The critical value at the level of significance: (Round to at least three decimal places.) Can we reject the aide's estimate that the proportion of college students who intend to vote is at most ? Yes No

Answer 1

Null hypothesis, the proportion who intend to vote in the upcoming election is at most 75%. p<=.75
Alternative hypothesis, the proportion who intend to vote in the upcoming election is greater than 75%. p>0.75

p-hat = X/n=   0.760    =209/275

test statistic, z = (phat-p)/sqrt(p*(1-p)/n)
z=(0.76-0.75)/SQRT(0.75*(1-0.75)/275)
z = 0.383

critical value, z(a)
z(0.1)
1.282

Since z < z(a), i fail to reject the null hypothesis. and conclude that the proportion who intend to vote in the upcoming election is at most 75%. p<=.75
NO.