Problem 2.1 Home cost The average cost of a single detached home in Pricy Town f

Question

Problem 2.1

Home cost The average cost of a single detached home in Pricy Town for 2014 is $482,000 with a standard deviation of $36,000. Let be the mean price of 49 houses. Find the probability that :

a. is greater than $492,000. [3 marks]

b. will fall between $476,000 and $488,000. [4 marks]

Problem 2.2.

Tuition fee A random sample of 30 full-time students form a large post-secondary institution was asked about their average tuition fee for the first year. From the data it was noted that the mean is $7850.00. The population standard deviation of the tuition fee is $257.00. Assume that the tuition fee is approximately normally distributed.

a. Construct an 80% confidence interval for µ. [3 marks]

b. Construct a 97% confidence interval for µ. [3 marks]

c. Refer to (a) and (b). What happens to the width of the confidence interval as the confidence level is increased (and everything else is kept the same)? [1 mark]

d. Refer to (a). Suppose you were not happy with the width of the confidence interval and wanted to cut the size of the interval to half, what should the sample size be? (Note: No calculation necessary!) [1 mark]

Explanation / Answer

We are allowed to do 1 question at a time. Post again for second question.

2.1)

a) z = (492,000 - 482,000)/36,000/49

z = 1.94

P (z > 1.94) = 0.026

b)

z = (476,000 - 482,000)/36,000/49

z = - 1.17

z = (488,000 - 482,000)/36,000/49

z = 1.17

P (-1.17 < z > 1.17) = 0.76

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