Exam 12: Inference About a Population

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When is the finite population correction used?

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If the sampled population is nonnormal,the t-test of the population mean μ\mu is still valid,provided that the condition is not extreme.

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A professor of statistics refutes the claim that the proportion of Republican voters in Michigan is at most 44%.To test the claim,the hypotheses: H0: p = 0.44,H1: p \neq 0.44,should be used.

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

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The air pumps at service stations come equipped with a gauge to regulate the air pressure of tires.A mechanic believes that the gauges are in error by at least 3 pounds per square inch.To test his belief he takes a random example of 50 air pump gauges and determines the difference between the true pressure (as measured by an accurate measuring device)and the pressure shown on the air pump gauge.The mean and the standard deviation of the sample are xˉ\bar { x } = 3.4 and s = 1.2.Can the mechanic infer that he is correct at the 5% significance level? Assume tire pressures have a normal distribution.

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

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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:

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When a population is small relative to the sample size,we must incorporate the ____________________ factor in the calculation of the standard error of estimate of the mean.

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If we are testing for an improvement in the consistency of an operation or the manufacturing of a product,the alternative hypothesis would have a(n)____________________ sign in it.

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The ____________________ confidence limit of the confidence interval estimator of the population variance is (n1)s2χα/22\frac { ( n - 1 ) s ^ { 2 } } { \chi _ { \alpha / 2 } ^ { 2 } } .

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Physicians A random sample of 200 physicians shows that there are 36 of them who make at least $400,000 a year. -{Physicians Narrative} Can we conclude at the 1% significance level that the true proportion of physicians in the population who make at least $400,000 a year is less than 0.24?

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

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When the population standard deviation is ____________________ and the population is normal,the test statistic for testing hypotheses about μ\mu is the t-distribution with n - 1 degrees of freedom.

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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.

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

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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. -{Mystic Pizza Narrative} We want to know whether Mystic can make this claim or not.Test to determine if we can infer at the 5% significance level that the population mean delivery time is less than 15 minutes.

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

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

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

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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[xˉ±tα/2s/n]N \left[ \bar { x } \pm t _ { \alpha / 2 } \cdot s / \sqrt { n } \right] .

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