Exam 12: Inference About a Population

If the lower and upper confidence limits of the population mean $\mu$ , using a sample of size 100, are 225 and 280, respectively, then the lower and upper confidence limits of the total of a population of size 3000 are respectively

The t-statistic has two variables: the sample ____________________ and the sample ____________________.

The t-distribution assumes that the population is normally distributed.

In a hypothesis test for the population variance, the hypotheses are H₀: $\sigma$ ² = 30 vs. H₁: $\sigma$ ² < 30. If the sample size is 20 and the test is being carried out at the 5% level of significance, the null hypothesis is rejected if:

Mass marketing is especially effective for ____________________ goods such as gasoline, which are difficult to differentiate from the competition except through price and availability.

The 95% confidence interval would indicate that, for this shipment, the proportion of defective fuses is between 0 and 0.28.

NARRBEGIN: Energy Drink Consumption 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.NARREND -{Energy Drink Consumption Narrative} Formulate the null and alternative hypotheses.

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} Explain how to use this confidence interval to test the hypotheses.

In estimating the total of a population of size N, where N is very large compared to the sample size, the confidence interval estimator of the total is $N \left[ \bar { x } \pm t _ { \alpha / 2 } \cdot s / \sqrt { n } \right]$ .

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} State the appropriate null and alternative hypotheses.

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} We want to test their claim and find out whether the actual percentage is not 10%. State the appropriate null and hypotheses.

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} Estimate with 95% confidence the total amount of monetary error for the month of July.

In determining the sample size needed to estimate the population proportion p, we let the sample proportion $\hat { p }$ = 1 if we have no knowledge of even the approximate values of $\hat { p }$ .

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

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} Estimate with 95% confidence the average amount of error per purchase order for the entire month of July.

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 -{Tire Rotation Narrative} What condition is required in order to analyze this data using a t-test?

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} What is the required condition of the techniques used in the previous questions? What graphical device can you use to check to see if that required condition is satisfied?

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 objective of this problem?

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

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