Exam 7: Sampling Distributions

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A sample that does not provide a good representation of the population from which it was collected is referred to as a (n) sample.

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The amount of tea leaves in a can from a production line is normally distributed with μ=110\mu = 110 grams and σ=25\sigma = 25 grams.A sample of 25 cans is to be selected.So, 95% of all sample meanswill be greater than how many grams?

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A study at a college in the west coast reveals that, historically, 45% of the students are minority students.If a random sample of size 75 is selected, the probability is that more than half of the students in the sample will be minority students.

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For sample size 1, the sampling distribution of the mean will be normally distributed

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The Central Limit Theorem is considered powerful in statistics because it works for any population distribution provided the sample size is sufficiently large and the population mean, and standard deviation are known.

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The standard error of the mean for a sample of 100 is 30.To cut the standard error of the mean to15, we would

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If the amount of gasoline purchased per car at a large service station has a population mean of 15 gallons and a population standard deviation of 4 gallons and a random sample of 4 cars is selected, there is approximately a 68.26% chance that the sample mean will be between 13 and 17 gallons.

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The amount of tea leaves in a can from a production line is normally distributed with μ=110\mu = 110 grams and σ=25\sigma = 25 grams.A sample of 25 cans is to be selected.What is the probability that thesample mean will be less than 100 grams?

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Suppose μ\mu = 50 and σ\sigma = 10 for a population.In a sample where n = 100 is randomly taken, 90% of all possible sample means will fall between 49 and 51.

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The amount of bleach a machine pours into bottles has a mean of 36 oz.with a standard deviation of 0.15 oz.Suppose we take a random sample of 36 bottles filled by this machine.The probability that the mean of the sample is between 35.95 and 35.98 oz.is .

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A sampling distribution is defined as the probability distribution of possible sample sizes that can be observed from a given population.

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The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes.A random sample of 16 cars is selected.What is the standard error of the mean?

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A study at a college in the west coast reveals that, historically, 45% of the students are minority students.If random samples of size 75 are selected, 95% of the samples will have more than% of minority students.

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SCENARIO 7-6 Online customer service is a key element to successful online retailing.According to a marketing survey, 37.5% of online customers take advantage of the online customer service.Random samples of 200 customers are selected. -Referring to Scenario 7-6, 95% of the samples that proportion symmetrically around the population proportion will have between % and % of the customers who take advantage of online customer service.

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For air travelers, one of the biggest complaints is of the waiting time between when the airplane taxis away from the terminal until the flight takes off.This waiting time is known to have a right skewed distribution with a mean of 10 minutes and a standard deviation of 8 minutes.Suppose100 flights have been randomly sampled.Describe the sampling distribution of the mean waiting time between when the airplane taxis away from the terminal until the flight takes off for these100 flights.

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SCENARIO 7-1 The time spent studying by students in the week before final exams follows a normal distribution with a standard deviation of 8 hours.A random sample of 4 students was taken to estimate the mean study time for the population of all students. -Referring to Scenario 7-1, what is the probability that the sample mean exceeds the population mean by more than 2 hours?

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If the population distribution is skewed, in most cases the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 30 observations.

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If the population distribution is unknown, in most cases the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 30 observations.

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Which of the following is true about the sampling distribution of the sample mean?

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As the sample size increases, the effect of an extreme value on the sample mean becomes smaller.

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