# Question: Consider Example 13 about testing H0 p 1 3 against

Consider Example 13 about testing H0: p = 1/3 against Ha: p > 1/3 for the astrology study, with n = 116. Find P(Type II error) for testing H0: p = 1/3 against Ha: p > 1/3 when actually p = 0.50, if the sample size is 60 instead of 116. Do this by showing that

a. The standard error is 0.061 when H0 is true.

b. The rejection region consists of p̂ values above 0.433.

c. When p = 0.50, the probability that p̂ falls below 0.433 is the left-tail probability below -1.03 under a standard normal curve. What is the answer? Why would you expect P(Type II error) to be larger when n is smaller?

a. The standard error is 0.061 when H0 is true.

b. The rejection region consists of p̂ values above 0.433.

c. When p = 0.50, the probability that p̂ falls below 0.433 is the left-tail probability below -1.03 under a standard normal curve. What is the answer? Why would you expect P(Type II error) to be larger when n is smaller?

## Answer to relevant Questions

Refer to the FL Student Survey data file on the text CD. Test whether the (a) Population mean political ideology (on a scale of 1 to 7, where 4 = moderate) equals or differs from 4.0. (b) Population proportion favoring ...According to the Bureau of Labor Statistics, the official unemployment rate was 15.5% among Blacks and 7.9% among Whites as of March 2011. During the recession of 2009–2011, the Black levels of unemployment have been ...The table summarizes results of a crossover study to compare results of low-dose and high-dose analgesics for relief of menstrual bleeding (B. Jones and M. Kenward, Statistics in Medicine, vol. 6, 1987, pp. 555–564). a. ...Refer to the FL Student Survey data file on the text CD. Using software, prepare a short report summarizing the use of confidence intervals and significance tests (including checking assumptions) to compare males and females ...The small-sample confidence interval for comparing two proportions is a simple adjustment of the large-sample one. Recall that for a small-sample confidence interval for a single proportion, we used the ordinary formula ...Post your question