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

Sales of a new line of athletic footwear are crucial to the success of a company. The company wishes to estimate the average weekly sales of the new footwear to within $200 with 95% Reliability. The initial sales indicate that the standard deviation of the weekly sales figures is Approximately $1400. How many weeks of data must be sampled for the company to get the Information it desires?

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 was calculated to be ($2,181,260, $5,836,180). Give a practical interpretation of the confidence interval.

Since the population standard deviation σ is almost always known, we use it instead of the sample standard deviation s when finding a confidence interval.

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

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 familyʹs 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 545 teenagers. Estimate the Proportion of all teenagers who want more family discussions about school. Use a 90% confidence Level.

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?

Which information is not shown on the screen below?

When the sample size is small, confidence intervals for a population proportion are more reliable when the population proportion p is near 0 or 1.

An educator wanted to look at the study habits of university students. As part of the research, data was collected for three variables - the amount of time (in hours per week)spent studying, the Amount of time (in hours per week)spent playing video games and the GPA - for a sample of 20 Male university students. As part of the research, a 95% confidence interval for the average GPA of All male university students was calculated to be: (2.95, 3.10). Which of the following statements is True?

A computer package was used to generate the following printout for estimating the mean sale price of homes in a particular neighborhood. A friend suggests that the mean sale price of homes in this neighborhood is $49,000. Comment on Your friendʹs suggestion.

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 Give a practical interpretation for the 95% confidence interval given above.

A local menʹs clothing store is being sold. The buyers are trying to estimate the percentage of items that are outdated. They will choose a random sample from the 100,000 items in the storeʹs inventory in order to determine the proportion of merchandise that is outdated. The current owners have never determined the percentage of outdated merchandise and cannot help the buyers. How large a sample do the buyers need in order to be 90% confident that the margin of error of their estimate is within 3%?

A random sample of $n = 144$ measurements was selected from a population with unknown mean $\mu$ and standard deviation $\sigma$ . Calculate a $90 \%$ confidence interval if $\bar { x } = 3.55$ and $s =$ 49

How much money does the average professional football fan spend on food at a single football game? That question was posed to 60 randomly selected football fans. The sampled results show That the sample mean was $70.00 and prior sampling indicated that the population standard Deviation was $17.50. Use this information to create a 95 percent confidence interval for the Population mean.

Suppose $( 1,000,2,100 )$ is a $95 \%$ confidence interval for $\mu$ . To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Explain why an increase in sample size will lead to a narrower interval of the estimate of $\mu$ .

The daily intakes of milk (in ounces)for ten five-year old children selected at random from one school were: 30.3 29.6 26.3 30.0 24.0 30.7 31.2 24.4 28.2 27.5 Find a $99 \%$ confidence interval for the standard deviation, $\sigma$ , of the daily milk intakes of all five-year olds at this school. Round to the nearest hundredth when necessary.

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): $60.2,47.0,235.1,490.0$ , 122.6, 177.5, 95.4, and 220.0. Summary statistics yield $\bar { x } = 180.975$ and $s = 143.042$ . Calculate a $95 \%$ confidence interval for the mean endowment of all private colleges in the United States.

We intend to estimate the average driving time of a group of commuters. From a previous study, we believe that the average time is 42 minutes with a standard deviation of 7 minutes. We want Our 90 percent confidence interval to have a margin of error of no more than plus or minus 4 Minutes. What is the smallest sample size that we should consider?

A local menʹs clothing store is being sold. The buyers are trying to estimate the percentage of items that are outdated. They will choose a random sample from the 100,000 items in the storeʹs Inventory in order to determine the proportion of merchandise that is outdated. The current Owners have never determined the percentage of outdated merchandise and cannot help the Buyers. How large a sample do the buyers need in order to be 99% confident that the margin of Error of their estimate is about 5%?