Exam 12: Inference About a Population

Energy Drink Consumption A researcher at the University of Washington medical school believes that energy drink consumption may increase heart rate.Suppose it is known that heart rate (in beats per minute) is normally distributed with an average of 70 bpm for adults.A random sample of 25 adults was selected and it was found that their average heartbeat was 73 bpm after energy drink consumption, with a standard deviation of 7 bpm. -{Energy Drink Consumption Narrative} Test the hypotheses in the previous question at the 10% significance level to determine if we can infer that energy drink consumption increases heart rate.

The ____________________ confidence limit of the confidence interval estimator of the population variance is .

Socialist Party Voters A pollster in Italy wants to challenge a claim that 5% of the registered voters in his country are Socialists; he thinks the percentage is lower than that.In a test of hypothesis, H₀: p = 0.05 vs.H₁: p < 0.05, his random sample of size 1,000 registered voters revealed that the number of Socialists was 40. -{Socialist Voters Narrative} Construct a 95% confidence interval estimate of the population proportion and explain how to use it to test the hypotheses.

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} Construct a 95% confidence interval estimate of the population proportion of the users of this allergy drug who experience drowsiness.

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} Compute the sample variance.

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. -A life insurance representative believes that the mean age of people who buy their first life insurance plan is less than 35.To test his belief he takes a random sample of 15 customers who have just purchased their first life insurance.Their ages are 42, 43,28, 34, 30, 36, 25, 29, 32, 33, 27, 30, 22, 37, and 40.There is not enough evidence to say the data are nonnormal.Can we conclude at the 1% significance level that the insurance representative is correct?

During a natural gas shortage, a gas company randomly sampled residential gas meters in order to monitor daily gas consumption.On a particular day, a sample of 100 meters showed a sample mean of 250 cubic feet and a sample standard deviation of 50 cubic feet.Provide a 90% confidence interval estimate of the mean gas consumption for the population.

In selecting the sample size to estimate the population proportion p, if we have no knowledge of even the approximate values of the sample proportion , we:

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} We want to test their claim and find out whether the actual percentage is not 10%.State the appropriate null and hypotheses.

A professor of statistics refutes the claim that the proportion of Republican voters in Michigan is at most 44%.To test the claim, the hypotheses: H₀: p = 0.44, H₁: p $\neq$ 0.44, should be used.

The test statistic for p is approximately normal when ____________________ and ____________________ are both greater than 5.

To test to see if the majority of the population exhibits a certain characteristic of interest, the alternative hypothesis of the test is H₁: p ____________________.

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} What is the objective of this problem?

In estimating the total of a population of size N, where N is very large compared to the sample size, the confidence interval estimator of the total is .

When is the finite population correction used?

Socialist Party Voters A pollster in Italy wants to challenge a claim that 5% of the registered voters in his country are Socialists; he thinks the percentage is lower than that.In a test of hypothesis, H₀: p = 0.05 vs.H₁: p < 0.05, his random sample of size 1,000 registered voters revealed that the number of Socialists was 40. -{Socialist Voters Narrative} Test the hypotheses at the 5% significance level.

The formula is used to find the sample size needed to estimate a population proportion.In this formula, B represents the ____________________ on the error of estimation.

If the sampled population is nonnormal, the t-test of the population mean $\mu$ is still valid, provided that the condition is not extreme.

A pharmaceutical company has just developed a new capsule to alleviate the symptoms of allergies and colds.However, they are concerned about the variability in the amount of time until the drug becomes effective.In a random sample of 10 individuals who suffer from allergies, the amount of time (in hours) for the capsule to take effect was recorded and listed as follows: 5, 7, 6, 10, 9, 12, 8, 17, 4, and 16.Estimate with 90% confidence the variance of the time for the drug to become effective.

In forming a 95% confidence interval for a population mean from a sample size of 20, the number of degrees of freedom from the t-distribution equals 20.