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 file vote.txt.

a) (5 marks) 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) (2 marks) Provide a formal interpretation of your p-value in a).

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

a) here X = 56

n = 100

p^ =X/n = 0.56

TS = (p^ - p)/(sqrT(pq/n)

=(0.56- 0.63)/sqrt(0.63*0.37/100)

= -1.4498627

p-value = 2 P(Z < -1.4498627)

=2*0.07350= 0.147

since p-value > 0.01

we fail to reject the null hypothesis

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