Exam 7: Inferences Based on a Single Sample: Estimation With Confidence Intervals

The following sample of 16 measurements was selected from a population that is approximately normally distributed. 61 85 92 77 83 81 75 78 95 87 69 74 76 84 80 83 Construct a 90% confidence interval for the population mean.

A study was conducted to determine what proportion of all college students considered themselves as full-time students. A random sample of 300 college students was selected and 210 of The students responded that they considered themselves full-time students. A computer program Was used to generate the following 95% confidence interval for the population proportion: (0.64814, 0.75186). Which of the following practical interpretations is correct for this confidence Interval?

A marketing research company is estimating the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 90% confidence interval for The mean was calculated to be ($2,181,260, $5,836,180). What additional assumption is necessary For this confidence interval to be valid?

Find the value of $t _ { 0 }$ such that the following statement is true: $P \left( - t _ { 0 } \leq t \leq t _ { 0 } \right) = .99$ where $\mathrm { df } = 9$ .

Suppose that 100 samples of size $n = 50$ are independently chosen from the same population and that each sample is used to construct its own $95 \%$ confidence interval for an unknown population mean $\mu$ . How many of the 100 confidence intervals would you expect to actually contain $\mu$ ?

The following data represent the scores of a sample of 50 randomly chosen students on a standardized test. 39 48 55 63 66 68 68 69 70 71 71 71 73 74 76 76 76 77 78 79 79 79 79 80 80 82 83 83 83 85 85 86 86 88 88 88 88 89 89 89 90 91 92 92 93 95 96 97 97 99 a. Write a 95% confidence interval for the mean score of all students who took the test. b. Identify the target parameter and the point estimator.

Parking at a large university can be extremely difficult at times. One particular university is trying to determine the location of a new parking garage. As part of their research, officials are interested In estimating the average parking time of students from within the various colleges on campus. A Survey of 338 College of Business (COBA)students yields the following descriptive information Regarding the length of time (in minutes)it took them to find a parking spot. Note that the ʺLo 95%ʺ and ʺUp 95%ʺ refer to the endpoints of the desired confidence interval. Variable N Lo 95\% CI Mean Up 95\% CI SD Parking Time 338 9.1944 10.466 11.738 11.885 University officials have determined that the confidence interval would be more useful if the Interval were narrower. Which of the following changes in the confidence level would result in a Narrower interval?

It is desired to estimate the average time it takes Statistics students to finish a computer project to within two hours at 90% reliability. It is estimated that the standard deviation of the times is 14 Hours. How large a sample should be taken to get the desired interval?

Suppose you wanted to estimate a binomial proportion, p, correct to within .05 with probability 0.95. What size sample would need to be selected if p is known to be approximately 0.8?

A random sample of 50 employees of a large company was asked the question, ʺDo you participate in the companyʹs stock purchase plan?ʺ The answers are shown below. yes no no yes no no yes yes no no no yes yes yes no yes no no yes yes no yes yes no yes yes no yes yes yes yes no no yes yes yes yes yes no yes no yes yes no yes yes yes yes yes yes Use a 90% confidence interval to estimate the proportion of employees who participate in the companyʹs stock purchase plan.

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 Students and finds that 118 of them are receiving financial aid. Use a 95% confidence interval to Estimate the true proportion of students who receive financial aid.

Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is invested in a fund called an endowment, and the College spends only the interest earned by the fund. A recent survey of eight private colleges in the United States revealed the following endowments (in millions of dollars): 88.9, 56, 249.3, 497, 124.7, 157.6, 108.9, and 222.8. What value will be used as the point estimate for the mean Endowment of all private colleges in the United States?

What type of car is more popular among college students, American or foreign? One hundred fifty-nine college students were randomly sampled and each was asked which type of car he or She prefers. A computer package was used to generate the printout below of a 90% confidence Interval for the proportion of college students who prefer American automobiles. SAMPLE PROPORTION $= .396$ SAMPLE SIZE $= 159$ UPPER LIMIT $= .460$ LOWER LIMIT $= .332$ Based on the interval above, do you believe that 31% of all college students prefer American Automobiles?

How much money does the average professional football fan spend on food at a single football game? That question was posed to 10 randomly selected football fans. The sample results provided A sample mean and standard deviation of $19.00 and $3.25, respectively. Use this information to Construct a 99% confidence interval for the mean.

Parking at a large university can be extremely difficult at times. One particular university is trying to determine the location of a new parking garage. As part of their research, officials are interested In estimating the average parking time of students from within the various colleges on campus. A Survey of 338 College of Business (COBA)students yields the following descriptive information Regarding the length of time (in minutes)it took them to find a parking spot. Note that the ʺLo 95%ʺ and ʺUp 95%ʺ refer to the endpoints of the desired confidence interval. Variable N Lo 95\% CI Mean Up 95\% CI SD Parking Time 338 9.1944 10.466 11.738 11.885 Explain what the phrase ʺ95% confidentʺ means when working with a 95% confidence interval.

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 Students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the Proportion of all students receiving financial aid to within 1% with 99% reliability, how many Students would need to be sampled?

A random sample of 4000 U.S. citizens yielded 2150 who are in favor of gun control legislation. Find the point estimate for estimating the proportion of all Americans who are in favor of gun Control legislation.

A computer package was used to generate the following printout for estimating the mean sale price of homes in a particular neighborhood. At what level of reliability is the confidence interval made?