Question

You are trying to estimate the confidence interval for the difference between two population means based on two independent samples of sizes n₁=24 and n₂=28. Which option below is NOT relevant for this case?

Select one:

a. To build the CI we have to obtain the critical value from a t-distribution with appropriate degrees of freedom.

b. To build the CI we have to estimate sample means based on each random sample.

c. To build the CI we have to estimate the overall sample variance based on the pooled dataset.

d. To build the CI we have to estimate sample variances based on each random sample.

Answer 1

To estimate the confidence interval for the difference between two population means based on two independent samples of sizes n₁=24 and n₂=28; we need

To build the CI we have to estimate sample means based on each random sample.

So; Option (b) is Relevant.

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2) Since the Population Variances are Unknown; so, we find the Pooled Variance using the the sample variances and samples size; which is denoted by

.Where

Therefore; to build the CI we have to estimate the overall sample variance based on the pooled dataset.

So; Option (c) is Relevant.

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3) To build the CI we have to obtain the critical value from a t-distribution with appropriate degrees of freedom.

can be 0.05 or 0.10

So; Option (a) is Relevant.

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To build the CI we don't need to estimate sample variances based on each random sample. So; Opton (d) is IRRELEVANT i.e NOT Relevant.

NOTE: Though we calculate the sample variances; it calculated to calculate the Pooled Variance.