Exam 12: Inference About a Population

When the population standard deviation is unknown and the population is ____________________, the test statistic for testing hypotheses about $\mu$ is the t-distribution with n - 1 degrees of freedom.

____________________ populations allow us to use the confidence interval estimate of a mean to produce a confidence interval estimate of the population total.

The formula is used to find the ____________________ to estimate a population proportion.

When the population standard deviation is unknown and the population is normal, the test statistic for testing hypotheses about $\mu$ is the ____________________-distribution with ____________________ degrees of freedom.

A race car driver tested his car for time from 0 to 60 mph, and in 20 tests obtained an average of 48.5 seconds with a standard deviation of 1.47 seconds.A 95% confidence interval for the 0 to 60 time is 45.2 seconds to 51.8 seconds.

Single Mothers' Ages A random sample of 10 single mothers was drawn from a Obstetrics Clinic.Their ages are 22, 17, 27, 20, 23, 19, 24, 18, 19, and 24 years. -{Single Mothers' Ages Narrative} What is the required condition of the techniques used in the previous questions? What graphical device can you use to check to see if that required condition is satisfied?

Applicants' Grades The grades of a sample of 10 applicants, selected at random from a large population, are 71, 86, 75, 63, 92, 70, 81, 59, 80, and 90. -{Applicants' Grades Narrative} Construct a 90% confidence interval estimate for the population variance.

Healthy Foods In segmenting the frozen meal market in Spain, a food manufacturer uses health and diet consciousness as the segmentation variable.Four segments are developed and coded as follows: To distinguish between groups, surveys are conducted.On the basis of a questionnaire, people are categorized as belonging to one of these groups.A recent survey asked a random sample of 1,500 Spanish adults (20 and over) to complete the survey.Out of the 1,500 people surveyed, 360 indicated that they are concerned about eating healthy foods.The most recent information available reveals that there are 40,256,000 Spanish adults who are 20 and over. -{Healthy Foods Narrative} Interpret the confidence interval of p.

Pilots' Union Contract A union composed of several thousand pilots is preparing to vote on a new contract.A random sample of 500 pilots yielded 320 who planned to vote yes.It is believed that the new contract will receive more than 60% yes votes. -{Pilots' Union Contract Narrative} State the appropriate null and alternative hypotheses.

When the population standard deviation is ____________________ and the population is normal, the test statistic for testing hypotheses about $\mu$ is the t-distribution with n -1 degrees of freedom.

In estimating the population mean $\mu$ when the population size N is small, the confidence interval estimator of $\mu$ is .

From a sample of 400 items, 14 are found to be defective.The point estimate of the population proportion defective will be:

New Mousetrap After a financial analysis, the general manager of a large company decided that if more than 8% of potential buyers of a new mousetrap purchase that product, the company would show a profit.In a preliminary survey of 500 potential buyers, 56 people say that they will buy the mousetrap. -{New Mousetrap Narrative} Is there sufficient evidence at the 5% significance level that the mousetrap will produce a profit?

Concert Tickets A simple random sample of 100 concert tickets was drawn from a normal population.The mean and standard deviation of the sample were $120 and $25, respectively. -{Concert Tickets Narrative} Test the hypothesis H₀: $\mu$ = 125 vs.H₁: $\mu$$\neq$ 125 at the 10% significance level.

The test statistic used to test hypotheses about the population variance has a(n) ____________________ distribution with ____________________ degrees of freedom.

Sinus Drug A company claims that 10% of the users of a certain sinus drug experience drowsiness.In clinical studies of this sinus drug, 81 of the 900 subjects experienced drowsiness -{Sinus Drug Narrative} Is there enough evidence at the 5% significance level to infer that the competitor is correct?

Tire Rotation The manager of a service station is in the process of analyzing the number of times car owners rotate the tires on their cars.She believes that the average motorist rotates his or her car's tires less frequently than recommended by the owner's manual (two times per year).In a preliminary survey she asked 14 car owners how many times they rotated their cars' tires in the last 12 months.The results are 1, 1, 2, 0, 3, 3, 0, 1, 0, 1, 2, 3, 3, and 1. -The air pumps at service stations come equipped with a gauge to regulate the air pressure of tires.A mechanic believes that the gauges are in error by at least 3 pounds per square inch.To test his belief he takes a random example of 50 air pump gauges and determines the difference between the true pressure (as measured by an accurate measuring device) and the pressure shown on the air pump gauge.The mean and the standard deviation of the sample are = 3.4 and s = 1.2.Can the mechanic infer that he is correct at the 5% significance level? Assume tire pressures have a normal distribution.

Hourly Fees A random sample of 15 hourly fees for car washers (including tips) was drawn from a normal population.The sample mean and sample standard deviation were = $14.9 and s = $6.75. -{Hourly Fees Narrative} Can we infer at the 5% significance level that the mean fee for car washers (including tips) is greater than 12?

In determining the sample size needed to estimate the population proportion p, we let the sample proportion = 1 if we have no knowledge of even the approximate values of .

Which of the following conditions is needed regarding the chi-squared test statistic for the test of variance?