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In: Statistics and Probability

Students studying at GWU spend an average of $172.50 per week on basic needs other than...

Students studying at GWU spend an average of $172.50 per week on basic needs other than housing. Use this figure as the population mean and assume that population standard deviation is $75.00.

  1. What is the probability that the mean expenditure for a sample of 35 students is within $20 of the population mean? What assumption do you need to make for this calculation?
  2. What is the probability that the mean expenditure for a sample of 50 students is within $20 of the population mean?
  3. What is the probability that the mean expenditure for a sample of 70 students is within $20 of the population mean?
  4. Which, if any, of the samples sizes in parts (a), (b), and (c) would you recommend in order to have at least a .95 probability that the sample mean is within $20 of the population mean?
  5. Using the standard error in c), calculate the value of x1, x2 such that P(x1 ≤ x ≤ x2) = .95 and express that result in terms of a range around the original population mean of $172.50. Hint: Use the conversion formula from z to x.

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orchestra answered 1 year ago
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