Exam 8: Confidence Intervals for One Population Mean

Find the specified t-value. -For a t-curve with df = 27, find the two t-values that divide the area under the curve into a middle 0.95 area and two outside areas of

Find the confidence interval specified. -A laboratory tested 85 chicken eggs and found that the mean amount of cholesterol was 190 milligrams. Assume that $\sigma = 11.7$ milligrams. Construct a $95 \%$ confidence interval for the true mean cholesterol content, $\mu$ , of all such eggs.

Write the word or phrase that best completes each statement or answers the question. -Suppose you wish to use the z-interval procedure to obtain a confidence interval for the population mean. If the sample size is large, but the data contain outliers, is it reasonable to use the z-interval procedure? How should you proceed?

Solve the problem. -A sample of 35 washing machines yields a mean replacement time of 9.0 years. Assuming that $\sigma$ = 2.4 years, find the margin of error in estimating $\mu$ at the 90% level of confidence.

Provide an appropriate response. -Suppose that you wish to obtain a confidence interval for a population mean. Under the conditions described below, should you use the z-interval procedure, the t-interval procedure, or neither? - The population standard deviation is unknown. - The population is normally distributed. - The sample size is small.

Find the value of $\alpha$ that corresponds to a confidence level of 81%.

Write the word or phrase that best completes each statement or answers the question. -Suppose that you wish to obtain a 95% confidence interval for a population mean. The population is normally distributed, the sample size is 20, and the population standard deviation is unknown. The correct procedure to use is the t-interval procedure. If you mistakenly use the z-interval procedure, will the resulting confidence interval be too wide or too narrow? Will the true confidence level associated with this interval be greater than or less than 95%?

Find the specified t-value. -For a t-curve with $\mathrm { df } = 15$ , find $\mathrm { t } _ { 0.025 } { } ^ { \text {. } }$

Write the word or phrase that best completes each statement or answers the question. -If the sample size is small (less than 15), under what conditions is it reasonable to use the z-interval procedure to obtain a confidence interval for the population mean? If the sample size is moderate (between 15 and 30), under what conditions is it reasonable to use the z-interval procedure to obtain a confidence interval for the population mean?

Write the word or phrase that best completes each statement or answers the question. -Scores on a test are normally distributed with a mean of 71 and a standard deviation of 11. For samples of size 35, which of the two variables below has more variation? Why? What is the distribution of each of the variables? (a) $\frac { \bar { x } - 71 } { 11 / \sqrt { 35 } }$ (b) $\frac { \bar { x } - 71 } { s / \sqrt { 35 } }$

A sample mean is used to estimate a population mean. To obtain a margin of error of 1.5 at a confidence level of 95%, a sample size of 120 is needed. Would the required sample size be larger or smaller if the researcher wished to (a)increase the confidence level while keeping the same margin of error? (b)decrease the margin of error while keeping the same confidence level? Explain your answers.

Find the requested confidence interval. -A random sample of 30 long distance runners aged 20-25 was selected from a running club. The resting heart rates (in beats per minute)of the runners are shown below. Estimate the mean resting Heart rate for the population of long distance runners aged 20-25. Assuming $\sigma$ = 8.03, give the 95.44% confidence interval for the population mean. 62 70 61 64 75 54 72 68 74 54 75 70 62 66 79 73 81 60 66 76 67 62 66 69 70 86 76 60 53 71

Find the necessary sample size. -Weights of women in one age group are normally distributed with a standard deviation Ϭ of 14 lb. A researcher wishes to estimate the mean weight of all women in this age group. Find how large a Sample must be drawn in order to be 90 percent confident that the sample mean will not differ from The population mean by more than 3.0 lb.

Find the confidence interval specified. Assume that the population is normally distributed. -A random sample of 30 households was selected from a particular neighborhood. The number of cars for each household is shown below. Estimate the mean number of cars per household for the Population of households in this neighborhood. Give the 95% confidence interval. 2 0 1 2 3 2 1 0 1 4 1 3 2 0 1 1 2 3 1 2 1 0 3 1 1 2 2 1 0 2

Find the specified t-value. -For a t-curve with df = 6, find the two t-values that divide the area under the curve into a middle 0.99 area and two outside areas of

Find the specified t-value. -For a t-curve with $\mathrm { df } = 4$ , find $\mathrm { t } _ { 0.05 }$ .

A sample of 81 women aged $18 - 24$ yields a mean systolic blood pressure of $114.6 \mathrm {~mm} \mathrm { Hg }$ . Assuming that $\sigma = 13.2 \mathrm {~mm} \mathrm { Hg }$ , find the margin of error in estimating $\mu$ at the $95 \%$ level of confidence.

Provide an appropriate response. -A confidence interval for a population mean has a margin of error of 2.2. If the sample mean is 51.3, obtain the confidence interval.

Find the specified t-value. -For a t-curve with $\mathrm { df } = 24$ , find $\mathrm { t } _ { 0.005 }$ . $^ { \text {. } }$

Find the necessary sample size. -The monthly earnings of a group of business students are are normally distributed with a standard deviation of 545 dollars. A researcher wants to estimate the mean monthly earnings of all business Students. Find the sample size needed to have a confidence level of 95% and a margin of error of 128 dollars.