Exam 9: Sampling Distributions

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The standard error of the sampling distribution of the sample proportion p~\tilde{ p } , when the sample size n = 100 and the population proportion p = 0.30, is 0.0021.

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NARRBEGIN: Heights of Men Heights of Men The heights of men in the USA are normally distributed with a mean of 68 inches and a standard deviation of 4 inches.NARREND -{Heights of Men Narrative} What is the probability that the mean height of a random sample of 36 men is greater than 70 inches?

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Suppose that 100 items are drawn from a population of manufactured products and the weight, X, of each item is recorded. Prior experience has shown that the weight has a non-normal probability distribution with μ\mu = 8 ounces and σ\sigma = 3 ounces. Which of the following is true about the sampling of Xˉ\bar { X } ?

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A sample of size n is selected at random from an infinite population. As n increases, the standard error of the sample mean increases.

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NARRBEGIN: Retirees Retirees A sample of 50 retirees is drawn at random from a normal population whose mean age and standard deviation are 75 and 6 years, respectively.NARREND -{Retirees Narrative} What is the probability that the mean age is at most 73 years?

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NARRBEGIN: Retirees Retirees A sample of 50 retirees is drawn at random from a normal population whose mean age and standard deviation are 75 and 6 years, respectively.NARREND -(Retirees Narrative} Find the mean and standard error of the sampling distribution of the sample mean.

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The expected value of the sampling distribution of Xˉ1Xˉ2\bar { X } _ { 1 } - \bar { X } _ { 2 } is μgˉ1xˉ2=μ1μ2\mu _ { \bar { g } _ { 1 } } - \bar { x } _ { 2 } = \mu _ { 1 } - \mu _ { 2 } where μ\mu i is the mean of population i (i = 1, 2).

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If two random samples of sizes n1 and n2 are selected independently from two populations with means μ\mu 1 and μ\mu 2, then the mean of Xˉ1Xˉ2\bar { X } _ { 1 } - \bar { X } _ { 2 } equals:

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The continuity correction factor adds and subtracts the number ____________________ to/from x to find P(X = x).

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NARRBEGIN: CFO's Salary CFO's Salary Suppose that the starting salaries of female CFO's have a positively skewed distribution with mean of $56,000 and a standard deviation of $12,000. The starting salaries of male CFO's are positively skewed with a mean of $50,000 and a standard deviation of $10,000. A random sample of 50 female CFO's and a random sample of 40 male CFO's are selected.NARREND -{CFO's Salary Narrative} Find the standard error of the sample mean difference.

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NARRBEGIN: Barack Obama Barack Obama Bill Clinton, the former President of the United States, believes that the proportion of voters who will vote for Barack Obama in the year 2012 presidential elections is 0.65. A sample of 500 voters is selected at random.NARREND -Let X be a binomial random variable with n = 100 and p = 0.7. Approximate the following probabilities, using the normal distribution. a.P(X = 75) b.P(X \le 70) c.P(X > 70)

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In general, the binomial probability P(X \le x) is approximated by the area under the normal curve to the left of x + .5.

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If the sample size increases, the standard error of the mean also increases.

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A sample of size 25 is selected at random from a finite population. If the finite population correction factor is 0.63, then the population size is:

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If two samples are selected independently from two non-normal populations, then the sampling distribution of Xˉ1Xˉ2\bar { X } _ { 1 } - \bar { X } _ { 2 } is only approximately normal provided that either n1 or n2 is 30 or more.

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NARRBEGIN: Barack Obama Barack Obama Bill Clinton, the former President of the United States, believes that the proportion of voters who will vote for Barack Obama in the year 2012 presidential elections is 0.65. A sample of 500 voters is selected at random.NARREND -{Barack Obama Narrative} Find the expected value and the standard deviation of the sample proportion p~\tilde{ p } .

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NARRBEGIN: PokerTime Poker Time The amount of time spent by American adults playing Poker per week is normally distributed with a mean of 4 hours and standard deviation of 1.25 hours.NARREND -{Poker Time Narrative} Find the probability that a randomly selected American adult plays Poker for more than 5 hours per week.

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A sample of size 25 is selected from a population of size 75. The finite population correction needed to find the standard error of Xˉ\bar { X } .

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The standard error of the sample proportion gets larger as:

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If all possible samples of size n are drawn from a population, the probability distribution of the sample mean Xˉ\bar { X } is called the:

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