The personnel department of a large corporation wants to estimate the family dental expenses of its employees to determine the feasibility of providing a dental insurance plan. A random sample of 12 employees in 2004 reveals the following family dental expenses (in dollars): 115, 370, 250, 93, 540, 225, 177, 425, 318, 182, 275, and 228. Use StatTools for your calculations.
(A) Construct a 90% confidence interval estimate of the mean family dental expenses for all employees of this corporation.
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(B) What assumption about the population distribution must be made to answer (A)?
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(C) Interpret the 90% confidence interval constructed in (A).
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(D) Suppose you used a 95% confidence interval in (A). Would this confidence interval be longer or shorter than the 90% confidence interval? Construct the 95% confidence interval.
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(E) Suppose the fourth value were 593 instead of 93. What would be your answer to (A)? What effect does this change have on the confidence interval?
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(F) Construct a 90% confidence interval estimate for the standard deviation of family dental expenses for all employees of this corporation.
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(G) Interpret the 90% confidence interval constructed in (E).
What will be an ideal response?
(A)
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(B) The population of dental expenses must be approximately normally distributed.
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(C) We are 90% confident that the mean family dental expenses for all employees of this corporation is between $199.26 and $333.74.
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(D) The confidence interval would be longer.
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(E)
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The additional $500 in dental expenses, divided across the sample of 12, raises the mean by $41.67 and increases the standard deviation by nearly $18.20. The interval width increases over $23 in the process.
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(F)
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