Exam 9: Sampling Distributions

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If two random samples of sizes 30 and 32 are selected independently from two populations with means 121 and 109, then the mean of the sampling distribution of the sample mean difference, Xˉ1Xˉ2\bar { X } _ { 1 } - \bar { X } _ { 2 } , equals 12.

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The owner of a meat market has an assistant who has determined that the weights of roasts are normally distributed, with a mean of 3.2 pounds and standard deviation of 0.8 pounds. If a sample of 25 roasts yields a mean of 3.6 pounds, what is the Z-score for this sample mean?

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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} What is the sampling distribution of the sample mean difference Xˉ1Xˉ2\bar { X } _ { 1 } - \bar { X } _ { 2 } ? Explain.

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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} What is the probability that the sample mean salary of male CFO's will not exceed that of the female CFO's?

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NARRBEGIN: Graduate Internships Graduate Internships The chairman of the Biology department in a certain college believes that 70% of the department's graduate internships are given to international students. A random sample of 50 graduate interns is taken.NARREND -{Graduate Internships Narrative} What is the probability that the sample proportion p~\tilde{ p } is between 0.65 and 0.73?

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For a sample size of 1, the sampling distribution of the mean is normally distributed:

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If the population is normal, then Xˉ\bar { X } is normally distributed for __________________ values of n.

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A sample of size 200 is taken at random from an infinite population. Given that the population proportion is 0.60, the probability that the sample proportion is between 0.58 and 0.62 is:

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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 exceeds 73 years?

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The amount of time it takes to complete a final examination is negatively skewed distribution with a mean of 70 minutes and a standard deviation of 8 minutes. If 64 students were randomly sampled, the probability that the sample mean of the sampled students exceeds 73.5 minutes is approximately 0.

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NARRBEGIN: Number of Fish Tanks Number of Fish Tanks The following data give the number of fish tanks owned for a population of 4 families. Family A B C D Number af Fish Tanks Owned 2 1 4 3 NARREND -{Number of Fish Tanks Narrative} Find the sampling distribution of Xˉ\bar { X } , and use it to calculate the mean and the standard deviation of Xˉ\bar { X } .

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NARRBEGIN: DVD Rental Store DVD Rental Store A DVD rental store wants to know what proportion of its customers are under age 21. A simple random sample of 500 customers was taken, and 375 of them were under age 21. Presume that the true population proportion of customers under age 21 is 0.68.NARREND -{DVD Rental Store Narrative} Describe the shape of the sampling distribution of proportion of customers who are under age 21.

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The expected value of the sampling distribution of the sample mean Xˉ\bar { X } equals the population mean μ\mu :

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NARRBEGIN: Graduate Internships Graduate Internships The chairman of the Biology department in a certain college believes that 70% of the department's graduate internships are given to international students. A random sample of 50 graduate interns is taken.NARREND -{Graduate Internships Narrative} What is the probability that the sample proportion p~\tilde{ p } is within ±\pm .05 of the population proportion p?

(Short Answer)
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