A presidential candidate\'s aide estimates that, among all college students, the

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 125 out of a random sample of 215 college students expressed an intent to vote, can we reject the aide's estimate at the 0.05 level of significance? Perform a one-tallied 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, consul a list of formulas.)

Explanation / Answer

The hypothesis formulation is as follows

Null hypothesis H0 p=P ,p0 is the hypothesized value of the population proportion.

Alternate hypothesis H1 : p |= P

= sqrt[ P * ( 1 - P ) / n ], so n = 215 and p = 125/215 = 0.581 and P = 0.60 (given)

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and is the standard deviation of the sampling distribution.

so sigma = sqrt(0.60*0.40/215) = 0.0334

The test statistic is a z-score (z) defined by the following equation.

z = (p - P) / =(0.581- 0.6)/0.0334 = - 0.5688

and the z critical for 0.05 is -1.6449 , as the z stat is less than z critical hence we fail to reject the null hypothesis

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