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

What is the confidence level of the following confidence interval for $\mu$ ? $\bar { x } \pm 1.645 \left( \frac { \sigma } { \sqrt { n } } \right)$

The U.S. Commission on Crime randomly selects 600 files of recently committed crimes in an area and finds 380 in which a firearm was reportedly used. Find a $95 \%$ confidence interval for $p$ , the true fraction of crimes in the area in which some type of firearm was reportedly used.

The confidence level is the confidence coefficient expressed as a percentage.

Explain what the phrase $95 \%$ confident means when we interpret a $95 \%$ confidence interval for $\mu$ .

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 for the proportion of College students who prefer American automobiles. SAMPLE PROPORTION $=.396226$ SAMPLE SIZE $=159$ UPPER LIMIT $=.46353$ LOWER LIMIT $=.331114$ Is the sample large enough for the interval to be valid?

If no estimate of p exists when determining the sample size for a confidence interval for a proportion, we can use .5 in the formula to get a value for n.

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 426 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. If the mean and standard deviation of the sample are $\bar { x } = 9.5$ hours and $s = 2.2$ hours, find a $99 \%$ confidence interval for the true mean number of hours a union member is absent per month. Round to the nearest thousandth.

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 ($146,132, $156,381). Give a practical interpretation of the interval.

A random sample of 250 students at a university finds that these students take a mean of $15.4$ credit hours per quarter with a standard deviation of $1.7$ credit hours. The $90 \%$ confidence interval for the mean is $15.4 \pm 0.177$ . Interpret the interval.

The standard deviation of a population is estimated to be 345 units. To estimate the population mean to within 49 units with 99% reliability, what size sample should be selected?

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 549 teenagers. Using 99% Reliability, can we say that more than 30% of all teenagers want to discuss school with their Parents?

The director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 64 different 24-hour Periods and determines the number of admissions for each. For this sample, x = 19.8 and s2 = 36. If The director wishes to estimate the mean number of admissions per 24-hour period to within 1 Admission with 90% reliability, what is the minimum sample size she should use?

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 $46,000. Comment on your friendʹs suggestion.

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). The researcher claimed that the Average GPA of all male students exceeded 2.94. Using the confidence interval supplied above, How do you respond to this claim?

A computer package was used to generate the following printout for estimating the mean sale price of homes in a particular neighborhood. Which of the following is a practical interpretation of the interval above?

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 confidence interval: (.438, .642). Using the information above, what sample size would be necessary if we wanted to estimate the True proportion to within 3% using 99% reliability?

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 99% confidence interval was calculated to be ($2,181,260, $5,836,180). Based on the interval above, do you believe the average total compensation of CEOs in the service industry is more than $1,500,000?

A random sample of 250 students at a university finds that these students take a mean of 15.8 credit hours per quarter with a standard deviation of 2.3 credit hours. Estimate the mean credit Hours taken by a student each quarter using a 90% confidence interval. Round to the nearest Thousandth.

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?