Question

1.

A facilities manager at a university reads in a research report that the mean amount of time spent in the shower by an adult is 5 minutes. He decides to collect data to see if the mean amount of time that college students spend in the shower is significantly different from 5 minutes. In a sample of 15 students, he found the average time was 4.29 minutes and the standard deviation was 0.75 minutes. Using this sample information, conduct the appropriate hypothesis test at the 0.01 level of significance. Assume normality.

a) What are the appropriate null and alternative hypotheses?

H0: ? = 5 versus Ha: ? ? 5H0: x = 5 versus Ha: x ? 5 H0: ? = 5 versus Ha: ? < 5H0: ? = 5 versus Ha: ? > 5

Answer 1

Null hypothesis
`H_0; \mu=5`

Alternative hypothesis
`H_a; \mu\\eq 5`

Explanation:

Consider the provided information.

The shower by an adult is 5 minutes.

The mean amount of time that college students spend in the shower is significantly different from 5 minutes. In a sample of 15 students, he found the average time was 4.29 minutes and the standard deviation was 0.75 minutes.

We need to determine the appropriate null and alternative hypotheses.

A null hypothesis is there is no statistical significance between the two variables.

An alternative hypothesis is there is a statistically significant relationship between two variables.

Therefore the required null and alternative hypothesis are:

Null hypothesis
`H_0; \mu=5`

Alternative hypothesis
`H_a; \mu\\eq 5`