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)

as i can not upload a txt file so the bottom data is the context in present in vote.txt .

1

0

0

1

1

0

1

0

0

0

1

1

1

0

1

0

1

1

0

0

1

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0

0

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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

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1

0

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1

Explanation / Answer

Null HYpothesis : H0 : p = 0.63

Alternative Hypothesis : Ha : p 0.63

Here p is the proportion of students who are in favour of the fee.

HEre sample proportion p^ = 56/100 = 0.56 (because there were 56 (1's) are there.

Test Statistic

standard error of the proportion se0 := Sqrt [p0 * (1-p0)/N] = sqrt [0.63 * 0.37 / 100] = 0.0483

so Z = (0.56 - 0.63)/ 0.0483 = -1.45

so P - value = Pr (Z < -1.45) = 0.145

and here we cannot reject the null hypothesis.

(b) Here p - vlaue is 0.145 that means that there are 14.5% probability is there that the proportion of people who favours a fee hike could be as far as (63 - 56 = 7%) both side when the mean proportion is 0.63

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