Exam 8: Sampling Distributions

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In order to estimate the mean salary for a population of 500 employees,the president of a certain company selected at random a sample of 40 employees.Would you use the finite population correction factor in calculating the standard error of the sample mean? Explain.

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Suppose an actual census showed that 18.4% of the households in California have incomes in excess of $50,000.The probability that the sample proportion will be 0.22 or greater for a random sample of 750 households is:

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Complete this equation: p= Number of successes  Answer 1= Answer 2n\mathrm { p } = \frac { \text { Number of successes } } { \text { Answer } 1 } = \frac { \text { Answer } 2 } { \mathrm { n } } Answer 1: ____________________ Answer 2: ____________________

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Each of the following are characteristics of the sampling distribution of the mean except:

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A population consisted of 500 cases involving shoplifters.If a random sample of 300 was taken and in 90 cases the offender was under age 18,in how many of the 500 cases would you say the person involved was under age 18? ____________________ cases

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The amount of time spent by American adults playing sports per day is normally distributed with a mean of 4 hours and standard deviation of 1.25 hours.Find the probability that if four American adults are randomly selected,their average number of hours spent playing sports is more than 5 hours per day.

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The heights of men in the USA are normally distributed with a mean of 68 inches and a standard of 4 inches.A random sample of five men is selected.What is the probability that the sample mean is greater than 70 inches?

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A trucking firm has trucks that average a payload of 22.5 tons and a standard deviation of 1.5 tons.An accounting firm is auditing the shipping orders for the past year for billing errors.It chooses a random sample of 64 shipping orders.What is the probability that the sample mean weight will be within 1 ton of the true population mean of 22.5 tons?

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A sample of size n is selected at random from an infinite population.As n increases,which of the following statements is true?

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The heights of men in the USA are normally distributed with a mean of 68 inches and a standard of 4 inches.What is the probability that a randomly selected man is taller than 70 inches?

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A normally distributed population with 200 elements has a mean of 60 and a standard deviation of 10.The probability that the mean of a sample of 25 elements taken from this population will be smaller than 56 is:

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Assume that all possible simple random samples of size two are taken from this population,and that the original population is normally distributed.Apply the Central Limit Theorem to find the mean of the sampling distribution of sample means.

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If a population is a Poisson distribution with a mean of 4,then the sampling distribution of the mean for 200 Excel or Minitab simulated samples approaches the normal distribution as the sample sizes are 5 or more.

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The average number of customers that visited a particular store during the past year is 160 per day and a standard deviation of 25 customers per day.A random sample of 64 days is chosen from this population.The standard deviation of the sample mean equals:

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Vehicles Four families live on a cul-de-sac represent a very small population.The number of vehicles owned by each family is shown below: Family = Number of vehicles Ali 1 Brown 1 Cosby 2 Davis 3 -Calculate the mean of the sample means.

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Sample data are used as the basis from which to make probability statements about the true (but unknown)value of the population mean or proportion.

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As a general rule,the normal distribution is used to approximate the sampling distribution of the sample proportion only if:

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The average SAT score for the 300 students accepted at Tiny College this year is 1050 with a standard deviation of 275.If a random sample of 40 students is selected from this class,what is the probability that the average SAT score will be greater than 1000?

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Determine which of the following population size and sample size combinations would require the use of the finite population correction factor in calculating the standard error. A)N = 150; n = 25 B)N = 1500; n = 300 C)N = 2500; n = 75 D)N = 15,000; n = 1000

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If young children watch an average of 105 minutes of TV per day with a standard deviation of 30 minutes per day,what is the probability that a random sample of 60 children will watch more than 110 minutes of TV per day?

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