Assume that a sample is used to estimate a population proportion p. Find the \( 98 \% \) confidence interval for a sample of size 228 with \( 75.9 \% \) successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places. \( 98 \% \) C.I. - Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

a. What is the difference between the number who prefer the cola to the lemon flavour? b. How many Grade 4D learners were questioned altogether?

A random sample of 69 produced the summary statistics \( \bar{x}=0.326 \) and \( \mathrm{s}^{2}=0.064 \). Complete parts a and \( b \). a. Test the null hypothesis that \( \mu=0.37 \) against the alternative hypothesis that \( \mu<0.37 \), using \( \alpha=0.10 \). What is the value of the test statistic? \( z=-1.44 \) (Round to two decimal places as needed.) Find the \( p \)-value. p-value \( =\square \) (Round to three decimal places as needed.)

A random sample of 69 produced the summary statistics \( \bar{x}=0.326 \) and \( s^{2}=0.064 \). Complete parts a and \( b \). State and interpret the results of the test. A. Reject \( H_{0} \). There is insufficient evidence to indicate that the true population mean is less than 0.37 at \( \alpha=0.10 \). Bo not reject \( H_{0} \). There is sufficient evidence to indicate that the true population mean is less than 0.37 at \( \alpha=0.10 \). C. Reject \( H_{0} \). There is sufficient evidence to indicate that the true population mean is less than 0.37 at \( \alpha=0.10 \). Do not reject \( H_{0} \). Thefe is insufficient evidence to indicate that the true population mean is less than 0.37 at \( \alpha=0.10 \).

University researchers published a working paper. One of the objectives of the study was to determine whether ride-share drivers actually make a profit. Data collected from a sample of 1,126 ride-share drivers yielded a mean monthly profit \( \bar{x}=\$ 661 \) with standard deviation \( s=\$ 581 \). A ride-share company executive reports that \( \mu \), the true mean monthly profit of all its rideshare drivers, is \( \$ 1,000 \). Use \( \alpha=0.01 \) to test the executive's figure. Complete parts a through e below. b. Find the rejection region for the test. Select the correct choice below and fill in the answer box(es) within your choice. (Round to two decimal places as needed.) A. \( z \) < \( z>\square \) C. \( z<\square \) or \( z>\square \)

The annual rainfall in a certain region is approximately normally distributed with mean 42.6 inches and standard deviation 5.7 inches. Round answers to the nearest tenth of a percent. a) What percentage of years will have an annual rainfall of less than 44 inches? b) What percentage of years will have an annual rainfall of more than 40 inches? c) What percentage of years will have an annual rainfall of between 39 inches and 43 inches? Question Help: \( \quad \) Read Video