Question

In each of the following exercises, formulate an appropriate null hypothesis and perform a test of that null hypothesis at the 5% and 1% significance levels. Use a one-sided or two-sided test as appropriate.

10. An instructor administers a 2-minute sit-up test to a class of 10 students, obtaining the following scores.
X : 55,45,48,62,58,60,42,44,53,55
The instructor expects students to have an average score of no more than 45 on the sit-up test. Part (a) Assume that 10 is the standard deviation of the sit-up test scores of all the coach’s past and present players.

Answer 1

Here the null hypothesis will be

against the alternative hypothesis will be

.

The mean of 10 students will be

= 52.2

.

The standard deviation is assumed as 10.

s = 10

The test statistic will be

=  2.27684

At level of significance 0.05

The critical value will be

from table

Reject null hypothesis if

.

Here

We accept null hypothesis .

At the level of significance = 0.01

The critical value will be

Reject null hypothesis if

.

Here

We accept null hypothesis .

There is no statistical evidence that the average score of students are no more than 45 on the sit-up test.