Suppose that a 95% confidence interval for a difference in population means base

Question

Suppose that a 95% confidence interval for a difference in population means based on samples of size n_1 = 100 and n_2 = 150 the percentiles of the difference for 1,000 bootstrap samples goes from 2.50 to 2.80. For each change described (with all else staying the same), indicate which of the three confidence intervals would be the most likely result. a. Increase the sample sizes to n_1 = 150 and n_2 = 200. A) 2.53 to 2.77 B) 2.50 to 2.80 C) 2.46 to 2.84 b. Decrease the confidence level to 90%. A) 2.53 to 2.77 B) 2.50 to 2.80 C) 2.46 to 2.84 c. Increase the number of bootstrap samples to 5,000 A) 2.53 to 2.77 B) 2.50 to 2.80 C) 2.46 to 2.84 The p-value is A) the probability that the null hypothesis is true. B) the probability that the alternative hypothesis is true. C) the probability, when the null hypothesis is true, of obtaining a sample as extreme as (or more extreme than) the observed sample. D) the probability, when the alternative hypothesis is true, of obtaining a sample as extreme as (or more extreme than) the observed sample. A Type I error occurs by A) rejecting the null hypothesis when the null hypothesis is false. B) not rejecting the null hypothesis when the null hypothesis is false. C) rejecting the null hypothesis when the null hypothesis is true. D) not rejecting the null hypothesis when the null hypothesis is true. Suppose that a 95% confidence interval for p is (54.8, 60.8). Which of the following is most likely the p-value for the test of H_0: Mu = 52 versus H_a: Mu notequalto 52?

Explanation / Answer

a) As the sample size increases, the interval and its width decrease, thus providing a more precise estimate of the population value. Option C 2.46 to 2.84

b) As the Confidence level decreases, the interval and its width decrease, thus providing a more precise estimate of the population value. In other words, in order to be less confident that our interval actually contains the population mean, we have to decreases the size of the interval. Option C 2.46 to 2.84

c) Option C 2.46 to 2.84

3) Option C the probability, when the null hypothesis is true, of obtaining a sample as extreme as the observed sample

4) Option C rejecting the null hypothesis when the null hypothesis is true

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