Exam 7: Confidence Intervals and Sample Size

A recent poll of 700 people who work indoors found that 278 smoke. If the researchers want to be 98% confident of their results to within 3.5 percentage points, how large a Sample is necessary?

If a population has a standard deviation of 14, what is the minimum number of samples that need to be averaged in order to be 95% confident that the average of the means is Within 5 of the true mean?

Find the 95% confidence interval for the variance of the heights of maple trees if a sample of 11 trees has a standard deviation of 10.2 feet.

7 squirrels were found to have an average weight of 8.7 ounces with a sample standard deviation is 1.1. Find the 95% confidence interval of the true mean weight.

Scores on the math SAT are normally distributed. A sample of 28 SAT scores had a standard deviation $s = 75$ . Construct a $99 \%$ confidence interval for the population standard deviation $\sigma$ .

Six measurements were made of the magnesium ion concentration (in parts per million, o in a city's municipal water supply, with the following results. It is reasonable to assume th population is approximately normal. 189 175 140 188 179 211 Construct a $98 \%$ confidence interval for the mean magnesium ion concentration.

A sample of size $n = 11$ has a sample mean $\bar { x } = 15.6$ and sample standard deviation $s = 2.4$ . Construct a $95 \%$ confidence interval for the population mean $\mu$ .

A food snack manufacturer samples 11 bags of pretzels off the assembly line and weighs their contents. If the sample mean is 15.2 oz. and the sample standard deviation is 0)50 oz., find the 95% confidence interval of the true mean.

A college admissions officer takes a simple random sample of 100 entering freshmen and computes their mean mathematics SAT score to be 459 . Assume the population standard deviation is $\sigma=103$ . Construct a $99 \%$ confidence interval for the mean mathematics SAT score for the enterin! freshmen class.

A simple random sample of kitchen toasters is to be taken to determine the mean operational lifetime in hours. Assume that the lifetimes are normally distributed with population standard deviation $\sigma = 20$ hours. Find the sample size needed so that a $98 \%$ confidence interval for the mean lifetime will have a margin of error of 8 .

The following MINITAB output presents a $95 \%$ confidence interval. The assumed sigma =7.9655 Variable Mean SE Mean 95\% 56 53.559 1.0644 (51.473,55.645) Find the sample size needed so that the $99 \%$ confidence interval will have a margin of err $1.1$ . rror of

A chi-square distribution is negatively skewed.

A study of 55 professors showed that the average time they spent creating test questions was 16.5 minutes per question. The standard deviation of the population is 5.8. Which Of the following is the 99% confidence interval for the average number of minutes it Takes to create a test question?

A researcher wants to construct a 99% confidence interval for the proportion of elementary school students in Seward County who receive free or reduced-price school Lunches. What sample size is needed so that the confidence interval will have a margin of Error of 0.07?

The following MINITAB output presents a confidence interval for a population mean. Variable Mean StDev SE Mean 99\% 72 84.4238 33.8186 3.9856 (73.874,94.973) How many degrees of freedom are there?

A sample of 41 light bulbs had a mean lifetime of 599 hours. A $95 \%$ confidence interval for the population mean was $593.8 < \mu < 604.2$ . Which one of the following statements is the correct interpretation of the results?

Find the point estimate for the given values of $x$ and $n$ . $x = 122 , n = 201$

A retailer wants to estimate with 99% confidence the number of people who shop at his store. A previous study showed that 24% of those interviewed had shopped at his store. He wishes to be accurate within 3% of the true proportion. The minimum sample size necessary would be 1,100.

A random sample of 9 TI-89 Titanium calculators being sold over the internet had the foll prices, in dollars. 142 149 147 146 145 148 154 136 131 Assume the population standard deviation is $\sigma = 30$ and that the population is approximat normal. Construct a $95 \%$ confidence interval for the mean price for all the TI-89's being sold over the internet. owing

A random sample of 75 printers discovered that 25 of them were being used in small businesses . Find the 99% limit for the population proportion of printers that are used in Small businesses.