A two-sided \(98\%\) normal confidence interval leaves equal probability in each tail of the standard normal distribution. What is the probability in each tail?

A normal population has known standard deviation \(20\). An independent random sample has size \(100\). Using \(z^*=1.96\), what is the margin of error of a \(95\%\) confidence interval for the population mean?

Using a valid method, a student calculates a \(95\%\) confidence interval \((18.2,21.8)\) for a population mean. Which statement gives the repeated-sampling interpretation of the method?

An independent random sample of \(49\) observations from a normal population has mean \(34\). The population standard deviation is known to be \(7\). Using \(z^*=1.96\), find a \(95\%\) confidence interval for the population mean.

Component lifetimes are normal with known standard deviation \(12\) hours. An independent random sample of \(16\) has mean \(180\) hours. Using \(z^*=1.645\), calculate a \(90\%\) confidence interval for the population mean, giving endpoints to 3 decimal places.

Normal confidence intervals use the same confidence level and the same known population standard deviation. If the independent random sample size increases from \(25\) to \(100\), what is the ratio of the new interval width to the old interval width?

An independent random sample has \(n=144\), \(\bar x=62\) and sample standard deviation \(s=24\), where \(s^2\) uses denominator \(n-1\). Population variance is unknown, and a large-sample normal approximation is suitable. Using \(z^*=2.576\), find an approximate \(99\%\) confidence interval for the population mean.

A normal population has known standard deviation \(9\). An independent random sample gives the \(95\%\) interval \((47.06,52.94)\), calculated using \(z^*=1.96\). Treat these displayed endpoints as the exact values obtained with that critical value. What was the sample size?

A normal population has known standard deviation \(11\). Independent random observations will be taken. Using \(z^*=1.645\), what is the smallest sample size giving a two-sided \(90\%\) confidence interval with full width at most \(5\)?

An independent random sample has \(n=100\), \(\sum x_i=4200\) and \(\sum x_i^2=179964\). The population variance is unknown, and a large-sample normal approximation is suitable. Use the unbiased variance estimate and \(z^*=1.96\) to find an approximate \(95\%\) confidence interval for the population mean. Give endpoints to 3 decimal places.