Hypothesis Testing

#1
Hi all,

I've got an MCQ question for uni that I'm not sure how to go about :confused:. If anyone could point me in the right direction that would be fantastic.

"A university administrator believes that less than 40% of full-time staff regularly use public transport to travel to the university. In a survey of 50 full-time staff, only 14 indicated that they regularly use public transport. On the basis of this evidence, the administrator would:

1. not reject the null hypothesis at the 5% level but reject it at the 1% level.
2. reject the null hypothesis at the 5% level but not at the 1% level.
3. reject the null hypothesis at both the 5% and 1% levels.
4. not reject the null hypothesis at both the 5% and 1% levels.

Thanks
 

Karabiner

TS Contributor
#2
You have one sample, a binary outcome and an hypothesis about the
proportion. Now you need to find and perform the appropriate test.

With kind regards

K.
 
#3
Since the hypothesis is that less than 40% of full-time staff regularly use public transport to travel to university, a one-tailed t-test should be conducted.

According to my statistical analysis, the data seems to have a z-value of -1.59 and a one-tailed p-value of 0.0539.

1) This is clearly not the answer because it is clearly self-evident that the p-value is within the scope of the 5% significance level (Not 1% level); however, it says not to reject the null-hypothesis which is wrong because it would actually lead to a Type II error. So 1 is not the answer.

2) Is the correct answer since the p-value is at the 5% level and not on the 1% level.

3) Is clearly not the answer because the p-value is not <0.01.

4) Is not the correct answer because the p-value is at the 5% significance level which means the null-hypothesis should be rejected.

So 2 is the correct answer.