Question

1.

a. What is the formula for standard error of a distribution of a sample proportion (sampling distribution of proportions)?

b. A distribution of a sample proportion (sampling distribution of proportions) is approximately normal if what 2 conditions are met?

c. What is the formula for standard error that is used to compute a confidence interval for a proportion?

d. What is the formula for standard error that is used to compute a test statistic for a proportion in a hypothesis test?

e. To conduct a hypothesis for a single mean using the t-distribution, we need one-two things to be true; the population must be approximately normal or the sample size is ______________. Fill in the blank with one word.

Answer 1

Solution:

a) The formula for standard error of a distribution of a sample proportion is as follows:

Where, P is population proportion and n is sample size.

Note: If population proportion (P) is not known we can use sample proportion (p̂) as the estimate of population proportion in the standard error formula.

b) If nP ≥ 10 and n(1 - P) ≥ 10, then the distribution of a sample proportion (sampling distribution of proportions) is approximately normal.

(Where, P is population proportion and n is sample size.)

c) The formula for standard error that is used to compute a confidence interval for a proportion is as follows:

Where, p̂ is sample proportion and n is sample size.

d) The formula for standard error that is used to compute a test statistic for a proportion in a hypothesis test is as follows:

Where, P is hypothesized value of population proportion and n is sample size.

e)  To conduct a hypothesis for a single mean using the t-distribution, we need one-two things to be true; the population must be approximately normal and the sample size is small.

Also the population standard deviation should be unknown.

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