Testing the hypothesis, it is found that:
a)
The null hypothesis is:
The alternative hypothesis is:
b)
The critical value is:
The decision rule is:
- If t < 1.74, we <u>do not reject</u> the null hypothesis.
- If t > 1.74, we <u>reject</u> the null hypothesis.
c)
Since t = 1.41 < 1.74, we <u>do not reject the null hypothesis</u>, that is, it cannot be concluded that the mean weight loss is of more than 10 pounds.
Item a:
At the null hypothesis, it is tested if the mean loss is of <u>at most 10 pounds</u>, that is:
At the alternative hypothesis, it is tested if the mean loss is of <u>more than 10 pounds</u>, that is:
Item b:
We are having a right-tailed test, as we are testing if the mean is more than a value, with a <u>significance level of 0.05</u> and 18 - 1 = <u>17 df.</u>
Hence, using a calculator for the t-distribution, the critical value is: .
Hence, the decision rule is:
- If t < 1.74, we <u>do not reject</u> the null hypothesis.
- If t > 1.74, we <u>reject</u> the null hypothesis.
Item c:
We have the <u>standard deviation for the sample</u>, hence the t-distribution is used. The test statistic is given by:
The parameters are:
is the sample mean.
is the value tested at the null hypothesis.
- s is the standard deviation of the sample.
- n is the sample size.
For this problem, we have that:
Thus, the value of the test statistic is:
Since t = 1.41 < 1.74, we <u>do not reject the null hypothesis</u>, that is, it cannot be concluded that the mean weight loss is of more than 10 pounds.
A similar problem is given at brainly.com/question/25147864