7 1/2 divided by (4 1/2 - 5 1/8) = ?
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Testing the hypothesis using the z-distribution, it is found that since the p-value of the test is of 0.0262 < 0.05, it <u>can be concluded that the new booklet is effective</u>.
At the null hypothesis, we <u>test if there has been no improvement</u>, that is, the time is still of 3 hours. Hence:
At the alternative hypothesis, we <u>test if there has been improvement</u>, that is, the time is of less than 3 hours. Thus:
We have the <u>standard deviation for the population</u>, thus, the z-distribution is used. The test statistic is given by:
The parameters are:
is the sample mean.
is the value tested at the null hypothesis.
is the standard deviation of the population.
- n is the sample size.
In this problem, the values of the parameters are: .
Then, the value of the test statistic is:
The p-value of the test is the probability of finding a sample mean of 2.9 hours or less, which is the <u>p-value of z = -1.94.</u>
Looking at the z-table, z = -1.94 has a p-value of 0.0262.
Since the p-value of the test is of 0.0262 < 0.05, it <u>can be concluded that the new booklet is effective</u>.
A similar problem is given at brainly.com/question/25413422