Question

Consider the following statements concerning confidence interval estimates: A. The use of the pooled variance estimator when constructing a confidence interval for the difference between means requires the assumption that the population variances are equal. B. The width of a confidence interval estimate for the proportion, or for mean when the population standard deviation is known, is inversely proportional to the square root of the sample size. C. To determine the sample size required to achieve a desired precision in the confidence interval estimate for the mean, the critical value for the standard normal distribution (ie. Z value) is required. only A is true only A and B are true only A and C are true only B and C are true A, B and C are true

Answer 1

Answer:-

Given That:-

Consider the following statements concerning confidence interval estimates:

A. The use of the pooled variance estimator when constructing a confidence interval for the difference between means requires the assumption that the population variances are equal.

B. The width of a confidence interval estimate for the proportion, or for mean when the population standard deviation is known, is inversely proportional to the square root of the sample size.

C. To determine the sample size required to achieve a desired precision in the confidence interval estimate for the mean, the critical value for the standard normal distribution (ie. Z value) is required.

only A is true only A and B are true only A and C are true only B and C are true A, B and C are true

Given,

The correct answer is A, B and C are true

For A

it is assumed that the population variance are equal when construction a confidence interval.

For B:

it is true that width is inversly proportional to the sqaure root of sample size.

Confidence interval width:-

Where

t = T - test statistic

n - 1 = Number of observations

= Significance level.

For C

Yes it is true that in order to determine the required sample size, it is necessary tio have the z xritical value. This will give the required precision of estimates.

so,

The correct answer is A, B and C are true

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