Exam 12: Inference About a Population

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?

NARRBEGIN: Single Mothers' Ages 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.NARREND -{Single Mothers' Ages Narrative} Estimate the population mean with 90% confidence.

The formula $\left( \frac { z _ { \alpha / 2 } \sqrt { \tilde { p } ( 1 - \tilde { p } ) } } { B } \right) ^ { 2 }$ is used to find the ____________________ to estimate a population proportion.

A left-tailed area in the chi-squared distribution equals 0.95. For 6 degrees of freedom the critical value equals 12.592.

If we have some idea about the value of sample proportion $\tilde{ p }$ , we use that value in determining the sample size needed to estimate the population proportion p.

The ____________________ confidence limit of the confidence interval estimator of the population variance is $\frac { ( n - 1 ) s ^ { 2 } } { \chi _ { 1 - \alpha / 2 } ^ { 2 } }$ .

NARRBEGIN: Tire Rotation 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.NARREND -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?

In testing a hypothesis about a population proportion p, the z test statistic measures how close the computed sample proportion $\tilde { p }$ has come to the hypothesized population parameter.

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.

NARRBEGIN: Science Quiz Scores Science Quiz Scores Consider the hypotheses H₀: $\sigma$ ² = 20 vs. H₁: $\sigma$ ² > 20. Assume that Science scores on a 25-point quiz for a random sample of 5 students were drawn from a normal population. These were: 18, 16, 10, 13, and 23.NARREND -An investor is concerned with the risk associated with a portfolio of stocks. He draws a random sample of nine monthly returns (expressed as a percentage of the initial investment). These data follow: 2, 5, -6, 10, 1, 2, -3, 0, and 7. Find a 95% confidence interval estimate of the population variance.

NARRBEGIN: Healthy foods 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: 1: Concermed about eating healthy faods 2: Concerned about weight 3: Concerned about health because of illnese 4: Unconcermed 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.NARREND -{Healthy Foods Narrative} What is the parameter we wish to estimate? Explain.

NARRBEGIN: Physicians Physicians A random sample of 200 physicians shows that there are 36 of them who make at least $400,000 a year.NARREND -{Physicians Narrative} Construct a 99% confidence interval estimate of the population proportion of physicians who make at least $400,000 a year, and explain how to use it to test the hypotheses.

A random sample of 25 observations is selected from a normally distributed population. The sample variance is 10. In the 95% confidence interval for the population variance, the upper limit is:

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

NARRBEGIN: Tire Rotation 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.NARREND -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 $\bar { x }$ = 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.

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

Mass Marketing refers to the mass production and marketing by a company of a single product for the entire market.

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: $\bar { x }$ = 52 and s = 22. Using the sample information provided, the value of the test statistic is:

Under what condition(s) does the test statistic for p have an approximate normal distribution?

A robust estimator is one that is: