Exam 7: Inferences Based on a Single Sample: Estimation With Confidence Intervals

A newspaper reports on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the familyʹs financial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 505 teenagers. Estimate the proportion of all teenagers who want more family discussions about religion. Use a 90% confidence level.

A random sample of 15 crates have a mean weight of $165.2$ pounds and a standard deviation of $13.5$ pounds. Construct a $95 \%$ confidence interval for the population standard deviation $\sigma$ . Assume the population is normally distributed, and round to the nearest hundredth when necessary.

A random sample of $\mathrm { n }$ measurements was selected from a population with unknown mean $\mu$ and known standard deviation $\sigma$ . Calculate a $95 \%$ confidence interval for $\mu$ for the given situation. Round to the nearest hundredth when necessary. $\mathrm { n } = 125 , \overline { \mathrm { x } } = 91 , \sigma = 20$

A confidence interval was used to estimate the proportion of statistics students who are female. A random sample of 72 statistics students generated the following 90% confidence interval: (.438, .642). Based on the interval, is the population proportion of females equal to 58%?

To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on this cigarette yielded a mean nicotine content of $25.9$ milligrams and standard deviation of $2.7$ milligrams for a sample of $n = 95$ cigarettes. Find a $95 \%$ confidence interval for $\mu$ .