Question

In: Statistics and Probability

Determine whether each of the following statements is true or false. Justify your answer for any...

Determine whether each of the following statements is true or false. Justify your answer for any that you think are false.

a) The margin of error for a 95% confidence interval for the population proportion p increases as the sample size increases.

b) The margin of error for a confidence interval for the population proportion p, based on a specified sample size n, increases as the confidence level decreases

. c) The margin of error for a 95% confidence interval for the population proportion p decreases as the percentage of successes decreases.

d) The p-value in a hypothesis test is the probability that the null hypothesis is true.

e) A type II error occurs in a hypothesis test when we falsely reject the null hypothesis.

Solutions

Expert Solution

a) The margin of error for a 95% confidence interval for the population proportion p increases as the sample size increases. -- false

since As sample size increases the margianl error decrease in the confidence interval for population proportion p

b) The margin of error for a confidence interval for the population proportion p, based on a specified sample size n, increases as the confidence level decreases - false

since the marginal error increases as confidence level increases

. c) The margin of error for a 95% confidence interval for the population proportion p decreases as the percentage of successes decreases. - TRUE

d) The p-value in a hypothesis test is the probability that the null hypothesis is true. FALSE.

A p-value is the probability of obtaining results as "extreme" or more "extreme" given that the null hypothesis is true.

e) A type II error occurs in a hypothesis test when we falsely reject the null hypothesis. FALSE

orchestra answered 1 year ago
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