Calculate a 95% confidence interval.

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Chapter 15, Problem 48CR

To determine

Calculate a 95% confidence interval.

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The use of the interval p̂ ± (z critical value) p̂(1 − p̂) n requires a large sample. For each of the following combinations of n and p̂, indicate whether the sample size is large enough for use of this interval to be appropriate. a. n = 51 and p̂ = 0.30 Yes or No b. n = 51 and p̂ = 0.05 Yes or No c. n = 11 and p̂ = 0.45 Yes or No

Consider the hypotheses shown below. Given that x=113, σ=27, n=42, α=0.10, complete parts a through c below. H0: μ=120 HA: μ≠120 a. State the decision rule in terms of the critical value(s) of the test statistic. Choose the correct answer in parenthesis. Reject the null hypothesis if the calculated value of the test statistic, (z, t) is (not contained within, not contained within, less than, equal to or greater than) the critical value(s), ___??___. Otherwise, do not reject the null hypothesis. (Round to two decimal places as needed. Use a comma to separate answers as needed.) b. State the calculated value of the test statistic. ***Hint: The test statistic for a hypothesis test of the population mean (when σ is known) can be calculated using technology or the formula shown below, where z is the z-test statistic, x is the sample mean, σ is the standard deviation of the population, n is the sample size, and μ is the mean of the sampling distribution, which is assumed…

The test statistic of z=−1.50 is obtained when testing the claim that p<0.76. a. Using a significance level of α=0.05, find the critical value(s). b. Should we reject H0 or should we fail to reject H0? a. The critical value(s) is/are z= (Round to two decimal places as needed. Use a comma to separate answers as needed.) b. Choose the correct conclusion below. A. Fail to reject H0. There is not sufficient evidence to support the claim that p<0.76. B. Reject H0. There is not sufficient evidence to support the claim that p<0.76. C. Reject H0. There is sufficient evidence to support the claim that p<0.76. D. Fail to reject H0. There issufficient evidence to support the claim that p<0.76.