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

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). The sample size that was used in this problem is considered a large sample. What criteria should be used to determine if n is large? A) If $\mathrm { n } \geq 30$ , then $\mathrm { n }$ is considered large. B) Both $\mathrm { n\hat {p} } \geq 15$ and $n\hat { q } \geq 15$ . C) If $n > 25$ , then $n$ is considered large. D) When working with proportions, any $n$ is considered large.

For data with two outcomes (success or failure), the binomial proportion of successes is likely to be the parameter of interest.

After elections were held, it was desired to estimate the proportion of voters who regretted that they did not vote. How many voters must be sampled in order to estimate the true proportion to within 2% (e.g., + 0.02) at the 90% confidence level? Assume that we believe this proportion lies close to 30%.

Let t0 be a specific value of t. Find t0 such that the following statement is true: $P \left( t \geq t _ { 0 } \right) = .025 \text { where df } = 20 \text {. }$

One way of reducing the width of a confidence interval is to reduce the confidence level.

A marketing research company is estimating which of two soft drinks college students prefer. A random sample of n college students produced the following 99% confidence interval for the proportion of college students who prefer drink A: (.265, .545). Identify the point estimate for estimating the true proportion of college students who prefer that drink.

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 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.

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 21% of all college students prefer American automobiles?

A random sample of 250 students at a university finds that these students take a mean of 15.6 credit hours per quarter with a standard deviation of 2.2 credit hours. Estimate the mean credit hours taken by a student each quarter using a 98% confidence interval. Round to the nearest thousandth. A) $15.6 \pm .324$ B) $15.6 \pm .219$ C) $15.6 \pm .021$ D) $15.6 \pm .014$

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?

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 90% 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 $12,320 with a standard deviation of $600. Suppose that the interval is calculated to be ($12,065.92, $12,574.08). How could we alter the sample size and the confidence coefficient in order to guarantee a decrease in the width of the interval?

Suppose you wanted to estimate a binomial proportion, p, correct to within .05 with probability 0.98. What size sample would need to be selected if p is known to be approximately 0.7?

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 90% confidence interval: (.438, .642). Based on the interval, is the population proportion of females equal to 59%?

Fifteen SmartCars were randomly selected and the highway mileage of each was noted. The analysis yielded a mean of 47 miles per gallon and a standard deviation of 5 miles per gallon. Which of the following would represent a 90% confidence interval for the average highway mileage of all SmartCars? A) $47 \pm 1.761 \frac { 5 } { \sqrt { 15 } }$ B) $47 \pm 1.345 \frac { 5 } { \sqrt { 15 } }$ C) $47 \pm 1.753 \frac { 5 } { \sqrt { 15 } }$ D) $47 \pm 1.645 \frac { 5 } { \sqrt { 15 } }$

Suppose a large labor union wishes to estimate the mean number of hours per month a union member is absent from work. The union decides to sample 343 of its members at random and monitor the working time of each of them for 1 month. At the end of the month, the total number of hours absent from work is recorded for each employee. Which of the following should be used to estimate the parameter of interest for this problem?

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 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 90% confidence interval to estimate the true proportion of students who receive financial aid. A) $.59 \pm .057$ B) $.59 \pm .002$ C) $.59 \pm .398$ D) $.59 \pm .004$

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 ($130,852, $147,990). 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?

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. Which of the following would represent the target parameter of interest?