Exam 7: Sampling Distributions

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In inferential statistics,the standard error of the sample mean assesses the uncertainty or error of estimation.

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A study at a college in the west coast reveals that,historically,45% of the students are minority students.The expected percentage of minority students in their next group of freshmen is .

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SCENARIO 7-3 The lifetimes of a certain brand of light bulbs are known to be normally distributed with a mean of 1,600 hours and a standard deviation of 400 hours.A random sample of 64 of these light bulbs is taken. -Referring to Scenario 7-3,the probability is 0.15 that the sample mean lifetime is more than how many hours?

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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 differs from the population mean by more than 3 hours?

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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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The Central Limit Theorem is important in statistics because

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At a computer manufacturing company,the actual size of a computer chip is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter.A random sample of 12 computer chips is taken.What is the standard error for the sample mean?

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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, _____% of the samples are likely to have less than 37.5% who take advantage of online customer service.

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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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At a computer manufacturing company,the actual size of a computer chip is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter.A random sample of 12 computer chips is taken.What is the probability that the sample mean will be between 0.99 and 1.01 centimeters?

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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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Suppose ? = 50 and σ\sigma = 10 for a population.In a sample where n = 100 is randomly taken,95% of all possible sample means will fall between 48.04 and 51.96.

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If the expected value of a sample statistic is equal to the parameter it is estimating,then we call that sample statistic

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The fact that the sample means are less variable than the population data can be observed from the standard error of the mean.

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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,the standard error of all possible sample proportions is .

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SCENARIO 7-5 According to an article,19% of the entire population in a developing country has high-speed access to the Internet.Random samples of size 200 are selected from the country's population. -Referring to Scenario 7-5,the population mean of all the sample proportions is .

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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 differs from the population mean by less than 2 hours?

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The standard deviation of the sampling distribution of a sample proportion is where π\pi is the population proportion.  The standard deviation of the sampling distribution of a sample proportion is where   \pi  is the population proportion.

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SCENARIO 7-3 The lifetimes of a certain brand of light bulbs are known to be normally distributed with a mean of 1,600 hours and a standard deviation of 400 hours.A random sample of 64 of these light bulbs is taken. -Referring to Scenario 7-3,the probability is 0.20 that the sample mean lifetime differs from the population mean lifetime by at least how many hours?

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The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed,with mean of 3.2 pounds and standard deviation of 0.8 pound.If a sample of 16 fish is taken,what would the standard error of the mean weight equal?

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