Two populations are described in each of the following cases. For each of the ca

Question

Two populations are described in each of the following cases. For each of the cases in parts a through e, would it be appropriate to apply the small-sample t-test to investigate the difference between the population means?

Bold a. nbspa.

sigma Subscript 1 Superscript 221.

sigma Subscript 2 Superscript 222equals=sigma Subscript 1 Superscript 221.

Choose the correct answer below.

Yes or No

Bold b. nbspb.

sigma Subscript 1 Superscript 221.

sigma Subscript 2 Superscript 222not equalssigma Subscript 1 Superscript 221.

Choose the correct answer below.

Yes or No

Bold c. c.

sigma Subscript 1 Superscript 221.

sigma Subscript 2 Superscript 222equals=sigma Subscript 1 Superscript 221.

Choose the correct answer below.

Yes or No

Bold d. d.

sigma Subscript 1 Superscript 221.

sigma Subscript 2 Superscript 222equals=sigma Subscript 1 Superscript 221.

Choose the correct answer below.

No or Yes

Bold e. e.

sigma Subscript 1 Superscript 221.

sigma Subscript 2 Superscript 222equals=sigma Subscript 1 Superscript 221.

Choose the correct answer below.

Yes or No

        

Bold a. nbspa.

Population 1: Normal distribution with variance

sigma Subscript 1 Superscript 221.

Population 2: Skewed to the right with variance

sigma Subscript 2 Superscript 222equals=sigma Subscript 1 Superscript 221.

Explanation / Answer

Since it is given that sample sizes are small so small sample t test both populations should be normally distributed

(a)

Here population 2 is skwed to right so we cannot apply small sample t test.

Answer: No

(b)

Here we can small sample t test (with unequal variances).

Anwer: yes

(c)

Populations are skewed so we cannot apply small sample t test.

Answer: No

(d)

Here we can small sample t test (with equal variances).

Anwer: yes

(e)

Populations are not normally distriuted so we cannot apply small sample t test.

Answer: No

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