Exam 12: Inference About a Population

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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: xˉ\bar { x } = 52 and s = 22.Suppose the alternative we wanted to test was H1: μ\mu < 60.The correct rejection region for α\alpha = 0.05 is:

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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. -{Healthy Foods Narrative} What is the point estimate of the proportion p of Spanish adults who classify themselves as concerned about eating healthy?

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

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A race car driver tested his car for time from 0 to 60 mph,and in 20 tests obtained an average of 48.5 seconds with a standard deviation of 1.47 seconds.A 95% confidence interval for the 0 to 60 time is 45.2 seconds to 51.8 seconds.

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A robust estimator is one that is:

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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 -{Sinus Drug Narrative} Compute the p-value of the test.

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Science Quiz Scores Consider the hypotheses H0: σ\sigma 2 = 20 vs.H1: σ\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. -{Science Quiz Scores Narrative} Estimate the population variance with 90% confidence.

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

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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: xˉ\bar { x } = $6.0 and s = $17.012. -{Tractor Dealership Narrative} Estimate with 95% confidence the average amount of error per purchase order for the entire month of July.

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The test statistic used to test hypotheses about the population variance has a chi-squared distribution with ____________________ degrees of freedom.

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

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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. -{Socialist Voters Narrative} Construct a 95% confidence interval estimate of the population proportion and explain how to use it to test the hypotheses.

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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. -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?

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A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches.To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90,a random sample of 100 doctors' results in 83 who indicate that they recommend aspirin.The value of the test statistic in this problem is approximately equal to:

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The ____________________ confidence limit of the confidence interval estimator of the population variance is (n1)s2χ1α/22\frac { ( n - 1 ) s ^ { 2 } } { \chi _ { 1 - \boldsymbol { \alpha } / 2 } ^ { 2 } } .

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Science Quiz Scores Consider the hypotheses H0: σ\sigma 2 = 20 vs.H1: σ\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. -{Science Quiz Scores Narrative} Test the hypotheses at the 10% significance level.

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

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

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

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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: xˉ\bar { x } = $6.0 and s = $17.012. -{Tractor Dealership Narrative} Estimate with 95% confidence the total amount of monetary error for the month of July.

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