Exam 12: Inference About a Population

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.

Generally speaking, mass marketing has given way to target marketing, which focuses on satisfying the demands of a particular segment of the entire market.

The statistic s² is an unbiased and consistent estimator of $\sigma$ ².

Researchers determined 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. Suppose the alternative we wanted to test was H₁: $\mu$ < 60. The correct rejection region for $\alpha$ = 0.05 is:

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

The test statistic for p is approximately normal when np and n(1 - p) are both ____________________.

NARRBEGIN: Applicants' Grades 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.NARREND -{Applicants' Grades Narrative} Construct a 90% confidence interval estimate for the population standard deviation.

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.

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.

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} Estimate with 95% confidence thee number of Spanish adults who classify themselves as concerned about eating healthy.

For a 99% confidence interval of the population mean based on a sample of n = 25 with s = 0.05, the critical value of t is:

Which of the following statements is correct regarding mass marketing?

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

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 -The sales manager of a large multinational corporation is concerned that some salespersons perform very well and others quite poorly. To help analyze the problem he draws a random sample of 20 salespersons, determines their commission incomes (in thousands of dollars), and calculates the following statistics: $\bar { x }$ = $37.2, and s = $7.8. Do these statistics provide sufficient evidence at the 5% significance level to conclude that the population variance exceeds $35 million²?

When determining the sample size needed for a proportion for a given level of confidence and sampling error, the closer to 0.50 that p is estimated to be:

NARRBEGIN: Applicants' Grades 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.NARREND -{Applicants' Grades Narrative} Compute the sample variance.

For statistical inference about the mean of a single population when the population standard deviation is unknown, the degrees for freedom for the t-distribution equal n -1 because we lose one degree of freedom by using the:

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} Compute the p-value and explain how to use it to test the hypotheses.

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} Test to determine if we can infer at the 5% significance level that the population mean is not equal to 20.

NARRBEGIN: Applicants' Grades 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.NARREND -{Applicants' Grades Narrative} Construct a 90% confidence interval estimate for the population variance.