Exam 8: Confidence Intervals for One Population Mean

Find the requested value. -A researcher wishes to estimate the mean resting heart rate for long-distance runners. A random sample of 12 long-distance runners yields the following heart rates, in beats per minute. 78 78 71 75 71 73 61 59 78 59 60 63 Use the data to obtain a point estimate of the mean resting heart rate for all long distance runners.

Is it true that the point estimate of a population mean must lie within the range of values defined by the corresponding confidence-interval estimate, regardless of the level of confidence achieved? Explain.

Find the requested value. -Physiologists often use the forced vital capacity as a way to assess a person's ability to move air in and out of their lungs. A researcher wishes to estimate the forced vital capacity of people suffering From asthma. A random sample of 15 asthmatics yields the following data on forced vital capacity, In liters. 5.2 3.4 2.9 5.3 3.0 4.0 5.2 5.2 3.2 4.7 3.2 3.5 4.8 4.0 5.1 Use the data to obtain a point estimate of the mean forced vital capacity for all asthmatics.

Find the confidence interval specified. Assume that the population is normally distributed. -The football coach randomly selected ten players and timed how long each player took to perform a certain drill. The times (in minutes)were: 12.9 13.3 13.3 7.7 11.7 9.9 12.5 6.5 10.8 12.2 Determine a 95% confidence interval for the mean time for all players.

Find the requested confidence interval. -A survey revealed the amount of pocket money held by each student in a sample of students from Statistics 205. The amounts (in dollars) are $5.50,10.20,3.15,6.08,4.85,4.80,4.70,8.52,7.90,6.10,3.50$ , $5.40,7.10,9.60,6.20$ , and $4.28$ . Assuming $\sigma = 2.00$ , find the $99.74 \%$ confidence interval for the population mean.

Find the confidence interval specified. Assume that the population is normally distributed. -A savings and loan association needs information concerning the checking account balances of its local customers. A random sample of 14 accounts was checked and yielded a mean balance of $664.14 and a standard deviation of $297.29. Find a 90% confidence interval for the true mean Checking account balance for local customers.

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 known. - The population is not normally distributed. - The sample size is 12.

Find the requested value. -A long-distance phone company wishes to estimate the mean duration of long-distance calls originating in California. A random sample of 15 long-distance calls originating in California Yields the following call durations, in minutes. 2 2 3 1 2 33 18 17 36 28 1 19 12 2 37 Use the data to obtain a point estimate of the mean call duration for all long-distance calls Originating in California.

Find the confidence interval specified. -30 people are selected randomly from a certain town. If their mean age is 60.5 and $\sigma$ = 4.6, find a 95% confidence interval for the true mean age, $\mu$ of everyone in the town.

Provide an appropriate response. -When estimating a population mean by a sample mean, which of the following does the margin of error not depend on?

Find the specified t-value. -For a t-curve with $\mathrm { df } = 23$ , find the $t$ -value having area $0.10$ to its left.

Find the specified t-value. -For a t-curve with $d f = 20$ , find $t _ { 0.01 }$ .

Provide an appropriate response. -Give an expression for the confidence level in terms of $\alpha$ .

Suppose that scores for men on an aptitude test have greater variability than scores for women on the same test. In other words, the population standard deviation is greater for the population of Men than for the population of women. Based on a sample of size 50, a 95% confidence interval for The mean score, $\mu ,$ , of all women has a margin of error of 2.2. Which of the following confidence Intervals will have a smaller margin of error? A. A 99% confidence interval for the mean score of women. Sample size = 50 B. A 95% confidence interval for the mean score of women. Sample size = 100 C. A 95% confidence interval for the mean score of men. Sample size = 50

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 data contain outliers. - The sample size is small.

Find the confidence interval specified. -The mean score, $\bar { x }$ , on an aptitude test for a random sample of 3 students was 65 . Assuming that $\sigma = 14$ , construct a $95.44 \%$ confidence interval for the mean score, $\mu$ , of all students taking the test.

Find the requested confidence interval. -The data below consists of the test scores of 32 students. Assuming $\sigma = 13.36$ , determine a $95.44 \%$ confidence interval for the population mean. 80 74 61 93 96 70 80 64 51 98 93 87 72 77 84 96 100 67 71 79 99 85 66 70 57 75 86 92 94 65 84 91

Write the word or phrase that best completes each statement or answers the question. -Compare the basic properties of t-curves with the basic properties of the standard normal curve. In what ways are t-curves similar to the standard normal curve? In what ways are they different?

Which of the following statements regarding t-curves is/are true? A. The total area under a t-curve with 10 degrees of freedom is greater than the area under the Standard normal curve. B. The t-curve with 10 degrees of freedom is flatter and wider than the standard normal curve. C. The t-curve with 10 degrees of freedom more closely resembles the standard normal curve than The t-curve with 20 degrees of freedom.

Find the confidence interval specified. Assume that the population is normally distributed. -Thirty randomly selected students took the calculus final. If the sample mean was 93 and the standard deviation was 13.3, construct a 99% confidence interval for the mean score of all students.