Exam 8: Confidence Interval Estimation

TABLE 8-4 The actual voltages of power packs labeled as 12 volts are as follows: 11.77, 11.90, 11.64, 11.84, 12.13, 11.99, and 11.77. -Referring to Table 8-4, a 90% confidence interval calculated from the same data would be narrower than a 99% confidence interval.

Suppose a 95% confidence interval for μ turns out to be (1,000, 2,100). Give a definition of what it means to be "95% confident" in an inference.

The t distribution allows the calculation of confidence intervals for means when the actual standard deviation is not known.

TABLE 8-5 A sample of salary offers (in thousands of dollars) given to management majors is: 48, 51, 46, 52, 47, 48, 47, 50, 51, and 59. Using this data to obtain a 95% confidence interval resulted in an interval from 47.19 to 52.61. -Referring to Table 8-5, 95% of the time, the sample mean salary offer to management majors will fall between 47.19 and 52.61.

When determining the sample size for a proportion for a given level of confidence and sampling error, the closer to 0.50 that π is estimated to be, the sample size required ________.

The t distribution is used to construct confidence intervals for the population mean when the population standard deviation is unknown.

TABLE 8-5 A sample of salary offers (in thousands of dollars) given to management majors is: 48, 51, 46, 52, 47, 48, 47, 50, 51, and 59. Using this data to obtain a 95% confidence interval resulted in an interval from 47.19 to 52.61. -Referring to Table 8-5, 95% of the salary offers are between 47.19 and 52.61.

A major department store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: = $50.50 and S² = 400. Assuming the distribution of the amount spent on their first visit is approximately normal, what is the shape of the sampling distribution of the sample mean that will be used to create the desired confidence interval for μ?

TABLE 8-11 A university wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students. A surveyed of 2,800 students was conducted and the students were asked if they felt comfortable reporting cheating by their fellow students. The results were 1,344 answered "Yes" and 1,456 answered "no." -Referring to Table 8-11, we are 99% confident that the total number of the student population who feel comfortable reporting cheating by their fellow students is between 0.4557 and 0.5043.

TABLE 8-2 A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. The desired length of the insulation is 12 feet. It is known that the standard deviation in the cutting length is 0.15 feet. A sample of 70 cut sheets yields a mean length of 12.14 feet. This sample will be used to obtain a 99% confidence interval for the mean length cut by machine. -Referring to Table 8-2, the confidence interval goes from ________ to ________.

TABLE 8-5 A sample of salary offers (in thousands of dollars) given to management majors is: 48, 51, 46, 52, 47, 48, 47, 50, 51, and 59. Using this data to obtain a 95% confidence interval resulted in an interval from 47.19 to 52.61. -Referring to Table 8-5, it is possible that the mean of the population is between 47.19 and 52.61.

The difference between the sample proportion and the population proportion is called the sampling error.

TABLE 8-5 A sample of salary offers (in thousands of dollars) given to management majors is: 48, 51, 46, 52, 47, 48, 47, 50, 51, and 59. Using this data to obtain a 95% confidence interval resulted in an interval from 47.19 to 52.61. -Referring to Table 8-5, 95% of all confidence intervals constructed similarly to this one with a sample size of 10 will contain the mean of the population.

An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What is the width of the 90% confidence interval?

TABLE 8-5 A sample of salary offers (in thousands of dollars) given to management majors is: 48, 51, 46, 52, 47, 48, 47, 50, 51, and 59. Using this data to obtain a 95% confidence interval resulted in an interval from 47.19 to 52.61. -Referring to Table 8-5, 95% of the sample means will fall between 47.19 and 52.61.

TABLE 8-9 The superintendent of a unified school district of a small town wants to make sure that no more than 5% of the students skip more than 10 days of school in a year. A random sample of 145 students from a population of 800 showed that 12 students skipped more than 10 days of school last year. -Referring to Table 8-9, the superintendent can conclude with 95% level of confidence that no more than 5% of the students in the unified school district skipped more than 10 days of school last year.

TABLE 8-3 To become an actuary, it is necessary to pass a series of 10 exams, including the most important one, an exam in probability and statistics. An insurance company wants to estimate the mean score on this exam for actuarial students who have enrolled in a special study program. They take a sample of 8 actuarial students in this program and determine that their scores are: 2, 5, 8, 8, 7, 6, 5, and 7. This sample will be used to calculate a 90% confidence interval for the mean score for actuarial students in the special study program. -Referring to Table 8-3, the critical value used in constructing a 90% confidence interval is ________.

TABLE 8-5 A sample of salary offers (in thousands of dollars) given to management majors is: 48, 51, 46, 52, 47, 48, 47, 50, 51, and 59. Using this data to obtain a 95% confidence interval resulted in an interval from 47.19 to 52.61. -Referring to Table 8-5, the confidence interval obtained is valid only if the distribution of the population of salary offers is normal.

A confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Using the information above, what total size sample would be necessary if we wanted to estimate the true proportion to within ±0.08 using 95% confidence?

TABLE 8-4 The actual voltages of power packs labeled as 12 volts are as follows: 11.77, 11.90, 11.64, 11.84, 12.13, 11.99, and 11.77. -Referring to Table 8-4, the critical value for a 99% confidence interval for this sample is ________.