Exam 12: Inference About a Population

A population is defined to be small if it is ____________________ than ____________________ times the size of the sample.

The width of a confidence interval estimate for a proportion will be:

A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the population mean would equal:

The chi-squared distribution can be used in constructing confidence intervals and carrying out hypothesis tests regarding the value of a population variance.

NARRBEGIN: Sinus Drug 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 NARREND -{Sinus Drug Narrative} Is there enough evidence at the 5% significance level to infer that the competitor is correct?

When is the finite population correction used?

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

After calculating the sample size needed to estimate a population proportion to within 0.04, your statistics professor told you the maximum allowable error must be reduced to just .01. If the original calculation led to a sample size of 800, the sample size will now have to be:

NARRBEGIN: Pilots' Union Contract 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.NARREND -{Pilots' Union Contract Narrative} Can we infer at the 5% significance level that the new contract will receive more than 60% yes votes?

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 ____________________.

NARRBEGIN: Concert Tickets 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.NARREND -{Concert Tickets Narrative} Explain how to use the confidence interval to test the hypotheses at $\alpha$ = 0.10.

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 point estimate of the proportion p of Spanish adults who classify themselves as concerned about eating healthy?

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 -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.

Market segmentation separates consumers of a product into different groups in such a way that members of each group are similar to each other and there are differences between groups.

To estimate ____________________ when the population size N is small, the confidence interval estimator is $\bar { x } \pm t _ { \omega / 2 } \cdot \frac { s } { \sqrt { n } } \sqrt { \frac { N - n } { N - 1 } }$ .

Because of the greater uncertainty, the t-statistic will display greater ____________________ than the z-statistic.

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 -{Science Quiz Scores Narrative} Test the hypotheses at the 10% significance level.

Mass marketing refers to the mass production and marketing by a company of all products the company produces for a single segment of the entire market.

In market segmentation, if education is the segmentation variable of interest, then possible segments of the market include: some high school, high school graduates, some college, college or university graduates.

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 -{Science Quiz Scores Narrative} Estimate the population variance with 90% confidence.