Exam 11: Inference About a Population

The sum of squared deviations from the mean divided by the population variance has a(n)____________________ distribution with ____________________ degrees of freedom.

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} Formulate the null and alternative hypotheses.

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 H ₀: m = 125 vs. H ₁: m ¹ 125 at the 10% significance level.

The statistic s² is an unbiased and consistent estimator of s ² .

In order to determine the p -value associated with hypothesis testing about the population mean m , it is necessary to know the value of the test statistic.

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

If we are testing for an improvement in the consistency of an operation or the manufacturing of a product, the alternative hypothesis would have a(n)____________________ sign in it.

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. {Tire Rotation Narrative} Does this data provide sufficient evidence at the 10% significance level to indicate that the manager is correct?

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.

Employees in a large company are entitled to 15-minute water breaks. A random sample of the duration of water breaks for 10 employees was taken with the times shown as: 12, 16, 14, 18, 21, 17, 19, 15, 18, and 16. Assuming that the times are normally distributed, is there enough evidence at the 5% significance level to indicate that on average employees are taking longer water breaks than they are entitled to?

The statistic when the sampled population is normal is Student t -distributed with n degrees of freedom.

Based on sample data, the 90% confidence interval limits for the population mean are LCL = 170.86 and UCL = 195.42. If the 10% level of significance were used in testing the hypotheses H ₀: m = 201 vs. H ₁: m ¹ 201, the null hypothesis:

Which of the following is not an example illustrating the use of variance?

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.

When a population is small, we must adjust the test statistic and interval estimator using the ____________________ population correction factor.

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?

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

The test statistic to test hypotheses about the population variance has a chi-squared distribution with n - 1 degrees of freedom when the population random variable has a(n)____________________ distribution.

If a sample has 15 observations and a 95% confidence estimate for m is needed, the appropriate value of t is 1.753.

Researchers determine that 60 Puffs tissues is the average number of tissues used during a cold. Suppose a random sample of 100 Puffs users yielded the following data on the number of tissues used during a cold: = 52 and s = 22. Using the sample information provided, the value of the test statistic is: