# Question: Recall that for the same sample size the smaller the

Recall that for the same sample size the smaller the probability of a Type I error, α, the larger the P(Type II error). Let’s check this for Example 13. There we found P(Type II error) for testing H0: p = 1>3 (astrologers randomly guessing) against Ha: p > 1 > 3 when actually p = 0.50, with n = 116. If we use α = 0.01, verify that:

a. A Type II error occurs if the sample proportion falls less than 2.326 standard errors above the null hypothesis value, which means p̂ < 0.435.

b. When p = 0.50, a Type II error has probability 0.08. (By comparison, Example 13 found P(Type II error) = 0.02 when α = 0.05, so we see that P(Type II error) increased when P(Type I error) decreased.)

a. A Type II error occurs if the sample proportion falls less than 2.326 standard errors above the null hypothesis value, which means p̂ < 0.435.

b. When p = 0.50, a Type II error has probability 0.08. (By comparison, Example 13 found P(Type II error) = 0.02 when α = 0.05, so we see that P(Type II error) increased when P(Type I error) decreased.)

**View Solution:**## Answer to relevant Questions

For testing H0: p = 1 / 3 (astrologers randomly guessing) against Ha: p > 1 / 3 with n = 116, Example 13 showed that P(Type II error) = 0.02 when p = 0.50. Now suppose that p = 0.35. Recall that P(Type I error) = 0.05. a. ...A person who claims to possess extrasensory perception (ESP) says she can guess more often than not the outcome of a flip of a balanced coin. Out of 20 flips, she guesses correctly 12 times. Would you conclude that she truly ...A fraternity at a university lobbies the administration to start a hockey team. To bolster its case, it reports that of a simple random sample of 100 students, 83% support starting the team. Upon further investigation, their ...Example 11 compared mean political beliefs (on a 1 to 7 point scale) to the moderate value of 4.0, using GSS data. Test whether the population mean equals 4.00 for females, for whom the sample mean was 3.98 and standard ...In making a decision in a significance test, a researcher worries about rejecting H0 when it may actually be true. a. Explain how the researcher can control the probability of this type of error. b. Why should the researcher ...Post your question