Question

QUESTION 1. The data for number of sleeping hours per day were recorded as below

A sample of 15 males has a sample mean of 7.3 hours and the population standard deviation is assumed to be 1.26 hours.

A sample of 18 females has a sample mean of 7.8 hours and the population standard deviation is assumed to be 1.51 hours.

1. a) Use the P-VALUE METHOD with a 0.08 significance level to test the claim that the mean number of sleeping hours for males is smaller than the mean number of sleeping hours for females.

2. b) What does the conclusion mean?

QUESTION 2. A simple random sample of 35 horrors has a mean duration of 107.3 minutes and the sample standard deviation of song lengths is 17.8 minutes.

Use a 0.05 significance level

1. a) Use the TRADITIONAL METHOD to test the claim that the sample is from a population of movies with a mean greater than 100 minutes.

2. b) What does the conclusion mean?

Answer 1

We would be looking at the first question, all parts here:

a) As we are testing here whether the mean number of sleeping hours for males is smaller than the mean number of sleeping hours for females, therefore the null and the alternative hypothesis here are given as:

A sample of 15 males has a sample mean of 7.3 hours and the population standard deviation is assumed to be 1.26 hours.

A sample of 18 females has a sample mean of 7.8 hours and the population standard deviation is assumed to be 1.51 hours.

The standard error is first computed here as:

The test statistic now is computed here as:

As this is a one tailed test, the p-value here is computed from the standard normal tables as:

p = P(Z < -1.0369) = 0.1499

As the p-value here is 0.1499 > 0.08 which is the level of significance, therefore the test is not significant and we cannot reject the null hypothesis here.

b) As the test is not significant, we dont have sufficient evidence here that the mean number of sleeping hours for males is smaller than the mean number of sleeping hours for females