Exam 6: Sampling and Sampling Distributions

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The standard error of the mean is also called sampling error.

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: It has been found that 62.1% of all unsolicited third class mail delivered to households goes unread.Over the course of a month,a household receives 100 pieces of unsolicited mail. -What is the mean of the sample proportion of pieces of unread mail?

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The average checking account balance at a local bank is $1,742 with a standard deviation of $132.A random sample of 70 accounts is selected. -The probability is 0.23 that the average balance for these accounts is greater than what amount?

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What is the probability that the sample proportion What is the probability that the sample proportion    will be between 0.65 and 0.73? will be between 0.65 and 0.73?

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The mean and variance of a chi-square distribution with ν degrees of freedom is determined by the number of degrees of freedom.

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: In a recent survey of high school students,it was found that the average amount of money spent on entertainment each week was normally distributed with a mean of $52.30 and a standard deviation of $18.23.Assume that these values are representative of all high school students. -What is the probability that for a sample of 25,the average amount spent exceeds $60?

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Random samples of size 36 each are taken from a large population whose mean is 120 and standard deviation is 39.The standard error of the sampling distribution of sample mean is:

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The sampling distribution of the mean is a distribution of:

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The number of nails in a five-pound box of nails is normally distributed with a mean of 563.3 and a standard deviation of 33.Suppose you select a random sample of 30 boxes. -What is the probability that the average number of nails per box for this sample is between 560 and 580 nails?

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose that 20% of all invoices are for amounts greater than $800.A random sample of 50 invoices is taken. -The average score of all students who took a particular statistics class last semester has a mean of 70 and a standard deviation of 3.0.Suppose 36 students who are taking the class this semester are selected at random.Find the probability that the average score of the 36 students exceeds 71.

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The central limit theorem states that as the sample size increases,the distribution of the population mean approaches the normal distribution.

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose you flip a coin four times.For every head,you receive one point,and for every tail,you lose one point. -What is the probability that the mean number of points you receive on four flips is 0.5?

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In a recent survey of high school students,it was found that the average amount of money spent on entertainment each week was normally distributed with a mean of $52.30 and a standard deviation of $18.23.Assuming these values are representative of all high school students,what is the probability that for a sample of 25,the average amount spent by each student exceeds $60?

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The sampling distribution of sample means is normal for samples of any size,n,provided that the parent sampled population has a normal distribution.

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The number of students using the ATM on campus daily is normally distributed with a mean of 237.6 and a standard deviation of 26.3.For a random sample of 55 days,what is the probability that the ATM usage averaged more than 230 students per day?

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The central limit theorem is basic to the concept of statistical inference because it permits us to draw conclusions about the population based strictly on sample data.

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The standard error of the sampling distribution of the sample proportion The standard error of the sampling distribution of the sample proportion    ,when the sample size n = 100 and the population proportion P = 0.30,is 0.0021 ,when the sample size n = 100 and the population proportion P = 0.30,is 0.0021

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The number of hours spent studying by students on Michigan State campus in the week before final exams follows a normal distribution with standard deviation 9.5 hours.A random sample of these students is taken to estimate the population mean number of hours studying. -Without doing the calculations,state whether a larger or smaller sample would be required to guarantee that the probability that the sample mean differs from the population mean by more than 1.8 hours is less than 0.05,when compared to the sample needed to ensure that the probability that the sample mean differs from the population mean by more than 2.1 hours is less than 0.05.

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The mean selling price of new homes in a city over a year was $120,000.The population standard deviation was $28,000.A random sample of 100 new home sales from this city was taken. -What is the probability that the sample mean selling price was more than $116,000?

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According to the central limit theorem,the sampling distribution of the sample mean can be approximated by the normal distribution as the:

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