At a certain university, support for the $200/year student activity fee has hist

Question

At a certain university, support for the $200/year student activity fee has historically been 63%. To investigate whether student opinion on this issue has changed, the Student Society polls 100 randomly sampled students and records their opinion (1=in favour of the fee, 0=opposed to the fee) in the vote file (Given Below).

a) Conduct a score test of whether the support for the activity fee has changed. Use a significance level of 1%. Be sure to state your null and alternative hypotheses, test statistic, p-value, and conclusion.

b) Provide a formal interpretation of your p-value in a).

VOTE FILE:

response
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1

Explanation / Answer

Question a)

Here,

x = 56

n = 100

p^ = 56 / 100 = 0.56

Null and Alternative Hypothesis:

H0: P = 0.56

H1: P ¹ 0.56

Level of significance = 0.1

Test Statistics:

z = (p^ - P)/sqrt((P*(1-P))/n)

   = (0.56 – 0.63)/sqrt((0.63*(1-0.63))/100)

   = -1.45

p-value = 2 * P ( z < -1.45)

               = 2 * normsdist(-1.45)

                = 2 * 0.0735

                = 0.1470

Here p-value is greater than the level of significance (0.1470>0.10); we fail to reject the null hypothesis. There is not sufficient evidence to conclude that the support for the activity fee has changed.

Question b)

Here the probability of finding observed, or more extreme, results when the null hypothesis (there is not sufficient evidence to conclude that the support for the activity fee has changed) is true is 14.70%.

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