Thread: Hypothesis question

Any help is appreciated; I am more or less just trying to figure out if I did this right.

Also for the question I have:
-stated the null and alternative hypothesis
-stated the critical region to reject or fail to reject the null
-Identified the test stat
-found the test stat
-stated the conclusion.

The question:
The transit company of a large city bases its fare on the assumption that 30% of riders pay reduced fares. A random sample of 1600 riders showed that 451 of them paid a reduced fare. At the 0.05 level of significance should the transit company continue to base fares on this assumption?

My answer:
Ho: p=0.30 H1: p=/=0.30
Critical region: Reject Ho if the test statisitc does not fall between 1.96 and -1.96. Fail to reject Ho if the test statistic falls between 1.96 and -1.96.
z=-1.75
test statistic = 0.0401*2=0.0802

There is not sufficient evidence to warrant rejection of the claim that 30% of its riders pay reduced fares.
Yes, the transit company should continue to base fares on this assumption.

Thanks in advance for you review! It is greatly appreciated.

Originally Posted by Thatgirl

Any help is appreciated; I am more or less just trying to figure out if I did this right.

Also for the question I have:
-stated the null and alternative hypothesis
-stated the critical region to reject or fail to reject the null
-Identified the test stat
-found the test stat
-stated the conclusion.

The question:
The transit company of a large city bases its fare on the assumption that 30% of riders pay reduced fares. A random sample of 1600 riders showed that 451 of them paid a reduced fare. At the 0.05 level of significance should the transit company continue to base fares on this assumption?

My answer:
Ho: p=0.30 H1: p=/=0.30
Critical region: Reject Ho if the test statisitc does not fall between 1.96 and -1.96. Fail to reject Ho if the test statistic falls between 1.96 and -1.96.
z=-1.75
test statistic = 0.0401*2=0.0802

There is not sufficient evidence to warrant rejection of the claim that 30% of its riders pay reduced fares.
Yes, the transit company should continue to base fares on this assumption.

Thanks in advance for you review! It is greatly appreciated.

I don't have time now to type the details, but I get a 95% confidence interval for the proportion of riders who pay reduced fares to be:

[0.271, 0.293].

0.30 lies outside this interval so I'd reject.

I might have time later to find your mistake.