Exam 12: Inference About a Population

A major electronics store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: $\bar { x }$ = $50.50 and s² = 400. A 95% confidence interval for the average amount the credit card customers spent on their first visit to the chain's new store in the mall is:

The t-distribution is used to develop a confidence interval estimate of the population mean when the population standard deviation is unknown.

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

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

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 the proportion p of Spanish adults who classify themselves as concerned about eating healthy.

NARRBEGIN: Hourly Fees 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 $\bar { x }$ = $14.9 and s = $6.75.NARREND -{Hourly Fees Narrative} Can we infer at the 5% significance level that the mean fee for car washers (including tips) is greater than 12?

Estimating or testing for p is used in situations when the data are ____________________.

The lower limit of the 90% confidence interval for the population proportion p, given that n = 400 and $\hat { p }$ = 0.10, is 0.0247.

NARRBEGIN: Tractor Dealership Tractor Dealership An accountant was performing an audit for a tractor dealership. An auditor wants to examine the monetary error made by the purchasing order department in the month of July. He decided to randomly sample 100 of the 925 purchase orders for the month of July, and found the amount of error in each one. The statistics for this sample were: $\bar { x }$ = $6.0 and s = $17.012.NARREND -{Tractor Dealership Narrative} Why should the finite population correction factor (FPCF) be used for this problem? Explain.

If a sample has 18 observations and a 90% confidence estimate for $\mu$ is needed, the appropriate value of t is 1.740.

NARRBEGIN: Socialist Voters 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.NARREND -{Socialist Voters Narrative} Compute the p-value and explain how to use it to test the hypotheses.

A random sample is drawn from a normal distribution with mean $\mu$ and variance $\sigma$ ². The random variable (n - 1)S² / $\sigma$ ² has a chi-squared probability distribution with n degrees of freedom.

Which of the following would be an appropriate alternative hypothesis?

NARRBEGIN: Mystic Pizza Mystic Pizza Mystic Pizza in Mystic, Connecticut, advertises that they deliver your pizza within 15 minutes of placing an order or it is free. A sample of 25 customers is selected at random. The average delivery time in the sample was 13 minutes with a sample standard deviation of 4 minutes.NARREND -{Mystic Pizza Narrative} What is the required condition of the technique used in the previous question?

Assuming that all necessary conditions are met, what needs to be changed in the formula $\tilde { p } \pm t _ { a } \sqrt { \tilde { p } ( 1 - \tilde { p } ) / n }$ so that we can use it to construct a (1 - $\alpha$ ) confidence interval estimate for the population proportion p?

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

The t-test for a population mean is ____________________, meaning that if the population is nonnormal, the results of the test and confidence interval are still valid as long as the nonnormality is not extreme.

The area to the right of a certain critical value on a chi-squared distribution is 0.025. For 5 degrees of freedom, the critical value is 11.143.

Two uses for the population variance are to measure risk and consistency.

To produce a confidence interval estimator for the total, we multiply the lower and upper confidence limits of the interval estimator of p by ____________________.