Question

The president of a university claims that the mean time spent partying by all students at this university is not more than 7 hours per week. A random sample of 30 students taken from this university showed that they spent an average of 9.50 hours partying the previous week with a standard deviation of 2.3 hours. Test at a significance level of 0.025 whether the president’s claim is true.

1. Write the null and the alternative hypothesis.
2. Calculate the test statistics.
3. Obtain the p-value.
4. Give your conclusion.

Answer 1

Write the null and the alternative hypothesis.

Here, we have to use one sample t test for the population mean.

The null and alternative hypotheses are given as below:

Null hypothesis: H0: the mean time spent partying by all students at this university is not more than 7 hours per week.

Alternative hypothesis: Ha: the mean time spent partying by all students at this university is more than 7 hours per week.

H0: µ ≤ 7 versus Ha: µ > 7

This is an upper tailed test.

Calculate the test statistics.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

t = (Xbar - µ)/[S/sqrt(n)]

t = (9.5 - 7)/[2.3/sqrt(30)]

t = 5.9535

Obtain the p-value.

P-value = 0.0000

(by using t-table)

P-value < α = 0.025

So, we reject the null hypothesis

Give your conclusion.

There is not sufficient evidence to conclude that the mean time spent partying by all students at this university is not more than 7 hours per week.

The president’s claim is not true.