Exam 6: Inferences Based on a Single Sample: Estimation With Confidence Intervals

A computer package was used to generate the following printout for estimating the mean sale price of homes in a particular neighborhood. X= saleprice SAMPLE MEAN OF X = 46300 SAMPLE STANDARD DEV = 13747 SAMPLE SIZE OF X = 25 CONEIDENCE = 90 UPPER LIMIT = 51003.90 SAMPLE MEAN OF X = 46300 LOWER LIMIT = 41596.10 A friend suggests that the mean sale price of homes in this neighborhood is $47,000. Comment on your friend's suggestion.

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.

Find the value of t0 such that the following statement is true: $P \left( - t _ { 0 } \leq t \leq t _ { 0 } \right) = .95 \text { where df } = 15$

Determine the confidence level for the given confidence interval for $\mu$ . $\bar { x } \pm 1.88 \left( \frac { \sigma } { \sqrt { n } } \right)$

A newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the family's financial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 508 teenagers. Estimate the proportion of all teenagers who want more family discussions about school. Use a 99% confidence Level.

A random sample of 4000 U.S. citizens yielded 2280 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. $X =$ sale_price SAMPLE MEAN OF X $= \quad 46,600$ SAMPLE STANDARD DEV $= 13,747$ SAMPLE SIZE OF X $= \quad 15$ CONFIDENCE $= \quad 95$ UPPER LIMIT $= 54,213.60$ SAMPLE MEAN OF X $= \quad 46,600$ LOWER LIMIT $= 38,986.40$ A friend suggests that the mean sale price of homes in this neighborhood is $48,000. Comment on your friend's suggestion.

You are interested in purchasing a new car. One of the many points you wish to consider is the resale value of the car after 5 years. Since you are particularly interested in a certain foreign sedan, you decide to estimate the resale value of this car with a 95% confidence interval. You manage to obtain data on 17 recently resold 5-year-old foreign sedans of the same model. These 17 cars were resold at an average price of $13,200 with a standard deviation of $700. Create a 95% confidence interval for the true mean resale value of a 5-year-old car of that model.

A random sample of 15 crates have a mean weight of 165.2 pounds and a standard deviation of 15.3 pounds. Construct a 95% confidence interval for the population standard deviation ?. Assume the population is normally distributed, and round to the nearest hundredth when necessary.

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 95% confidence interval for the proportion of college students who prefer American automobiles. SAMPLE PROPORTION $= .396$ SAMPLE SIZE $= 159$ UPPER LIMIT $= .472$ LOWER LIMIT $= .320$ Which of the following is a correct practical interpretation of the interval?

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): 77.8, 45.1, 243.4, 489.5, 113.9, 187.6, 102.4, and 210.2. What value will be used as the point estimate for the mean endowment of all private colleges in the United States?

A random sample of 50 employees of a large company was asked the question, "Do you participate in the company's stock purchase plan?" 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 company's stock purchase plan.

A retired statistician was interested in determining the average cost of a $200,000.00 term life insurance policy for a 60-year-old male non-smoker. He randomly sampled 65 subjects (60-year-old male non-smokers) and constructed the following 95 percent confidence interval for The mean cost of the term life insurance: ($850.00, $1050.00). State the appropriate interpretation for this confidence interval. Note that all answers begin with "We are 95 percent confidence that…"

A confidence interval was used to estimate the proportion of statistics students who are female. A random sample of 72 statistics students generated the following 99% confidence interval: (.438, .642). State the level of reliability used to create the confidence interval.

A random sample of 80 observations produced a mean $\bar { x } = 35.4$ and a standard deviation $= 3.1$ . a. Find a $90 \%$ confidence interval for the population mean $\mu$ . b. Find a $95 \%$ confidence interval for $\mu$ . c. Find a $99 \%$ confidence interval for $\mu$ . d. What happens to the width of a confidence interval as the value of the confidence coefficient is increased while the sample size is held fixed?

Given the values of $\bar { x } , \mathrm {~s}$ , and $n$ , form a $99 \%$ confidence interval for $\sigma ^ { 2 }$ . $\bar { x } = 16.9 , \mathrm {~s} = 8.6 , \mathrm { n } = 24$

A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($133,306, $150,733). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced interval width?

A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($110,389, $128,192). Give a practical interpretation of the interval.

For the given combination of $\alpha$ and degrees of freedom $( \mathrm { df } )$ , find the value of $\chi _ { ( 1 - \alpha / 2 ) } ^ { 2 }$ that would be used to find the upper endpoint of a confidence interval for $\sigma ^ { 2 }$ . $\alpha = 0.01 , \mathrm { df } = 6$

Suppose the population standard deviation is known to be $\sigma = 150$ . Calculate the standard error of $\bar { x }$ when $n = 300$ and $N = 1500$ .