Question

A study compared weight loss between patients on diet A and patients on diet B. Let

mu 1μ1

represent the mean of number of pounds patients on diet A lose in six months and

mu 2μ2

represent the mean of number of pounds patients on diet B lose in six months. Complete parts​ (a) through

​(d).

a. State the null and alternative hypotheses if you want to test whether the mean weight loss between the two diets is equal. What are the null and alternative​ hypotheses?

A.

Upper H 0H0​:

mu 1 equals mu 2μ1=μ2

Upper H 1H1​:

mu 1 not equals mu 2μ1≠μ2

B.

Upper H 0H0​:

mu 1μ1less than or equals≤mu 2μ2

Upper H 1H1​:

mu 1μ1greater than>mu 2μ2

C.

Upper H 0H0​:

mu 1μ1greater than or equals≥mu 2μ2

Upper H 1H1​:

mu 1μ1less than<mu 2μ2

D.

Upper H 0H0​:

mu 1 not equals mu 2μ1≠μ2

Upper H 1H1​:

mu 1 equals mu 2μ1=μ2

b. In the context of this​ study, what is the meaning of a Type I​ error?

A.

A Type I error is committed when the null hypothesis is rejected when there is a significant difference in the mean weight loss between the two diets.

B.

A Type I error is committed when one concludes that there is a significant difference in mean weight loss between the two diets when there is not a significant difference.

C.

A Type I error is committed when one rejects both the null and alternative hypotheses.

D.

A Type I error is committed when one concludes that there is not a significant difference in mean weight loss between the two diets when there is a significant difference.

c. In the context of this​ study, what is the meaning of a Type II​ error?

A.

A Type II error is committed when one does not reject both the null and the alternative hypothesis.

B.

A Type II error is committed when one concludes that there is not a significant difference in mean weight loss of only diet A.

C.

A Type II error is committed when one concludes that there is not a significant difference in mean weight loss between the two diets when there is indeed a significant difference.

D.

A Type II error is committed when one concludes that there is a significant difference in mean weight loss between the two diets when there is not a significant difference.

d. Suppose that a sample of

108108

patients on diet A lost a mean of

7.37.3

pounds in six​ months, with a sample standard deviation of

3.83.8

​pounds, whereas a sample of

108108

patients on diet B lost a mean of

7.47.4

pounds in six​ months, with a standard deviation of

2.52.5

pounds. Assume the population variances are equal. Using a

0.050.05

level of​ significance, is there evidence of a difference in the mean weight loss of patients between the two​ diets?

▼

Do not reject

Reject

H0.

There

▼

is insufficient evidence

is evidence

of a difference in the mean weight loss of patients between the two diets.

Answer 1

1. The following null and alternative hypotheses need to be tested:

OPTION A

2. Type 1 error happens when

OPTION B.

A Type I error is committed when one concludes that there is a significant difference in mean weight loss between the two diets when there is not a significant difference.

3.

DO NOT REJECT

is insufficient evidence

Since it is assumed that the population variances are equal, the t-statistic is computed as follows:

Since it is observed that ∣t∣=0.228≤tc​=1.971, it is then concluded that the null hypothesis is not rejected

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