Question

A presidential candidate's aide estimates that, among all college students, the proportion p who intend to vote in the upcoming election is at least 60%. If 118 out of a random sample of 225 college students expressed an intent to vote, can we reject the aide's estimate at the 0.05 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: H0: The alternative hypothesis: H1: The type of test statistic: (Choose one)ZtChi squareF The value of the test statistic: (Round to at least three decimal places.)

Answer 1

A presidential candidate's aide estimates that, among all college students, the proportion p who intends to vote in the upcoming election is at least 60% so population proportion p_o= 0.60.

so, the claim is p_o>=0.60.

Now given that  X = 118 out of a random sample of n = 225 college students expressed an intent to vote, so the sample proportion will be:

Now to check the normality condition for hypothesis testing the condition is:

p_o*(1-p_o)*n >=10

so, 0.60(1-0.60)*225 = 54 which is greater than 10 so, assuming normal distribution Z test is applicable, based on the claim the hypotheses are:

a) Ho: p>=0.60

Ha: p<0.60

b) Based on the hypothesis it will be left tailed test. ( Z Test)

c)Test Statistic:

The test statistic is calculated as:

Rejection region:

At 0.05 level of significance, the critical value is computed using excel formula for normal distribution which is =NORM.S.INV(0.05), thus Zc computed as 1.645.

So, reject Ho if Z <Zc or the P-value is less than 0.05

P-value:

The P-value is computed using excel formula =NORM.S.DIST(-2.313,TRUE) which results in P-value = 0.0104.

Conclusion:

Since P-value is less than 0.05 and Z is less than Zc hence we reject the null hypothesis and conclude that there is sufficient evidence to warrant the claim that the proportion p who intends to vote in the upcoming election is at least 60%.