Answer to Question #271511 in Statistics and Probability for Dunken

Question

It is claimed that the average time it takes high school seniors to complete a standardized

test is more than 30 minutes. A random sample of 24 high school seniors took an average

of 30 minutes to complete this test with a standard deviation of 3 minutes. Test the claim

at 1% level of significance.

Answer 1

Null hypothesis $H_0:\mu=30.$

Alternative hypothesis $H_a:\mu>30.$

Test statistic: $t=\frac{\bar x-\mu}{\frac{s}{\sqrt{n}}}=\frac{30-30}{\frac{3}{\sqrt{24}}}=0.$

Degrees of freedom: $df=n-1=24-1=23.$

P-value: $p=P(T>0)=0.5.$

Since the p-value is greater than 0.01, fail to reject the null hypothesis.

There is no sufficient evidence that the average time it takes high school seniors to complete a standardized test is more than 30 minutes.