18. Hours Spent Studying A university dean wishes to estimate the average number

Question

18. Hours Spent Studying A university dean wishes to estimate the average number of hours that freshmen study each week. The standard deviation from a previous st udy is 2.6 hours. How large a sample must be selected if he wants to be 99% confident of finding whether the true mean differs from the sample mean by 0.5 hour? 19. Money Spent on Road Repairs A researcher wishes to estimate within $300 the true average amount of money a county spends on road repairs each year. If she wants to be 90% confident, how large a sample is necessary? The standard deviation is known to be $900

Explanation / Answer

18) Step 1: Find z a/2 by dividing the confidence interval by two, and looking that area up in the z-table:

.99/2 = 0.495. The closest z-score for 0.495 is 2.58.

Step 2: Multiply step 1 by the standard deviation.
2.58 * 2.6 = 6.708

Step 3: Divide Step 2 by the margin of error. Our margin of error (from the question), is 0.5.

6.708/0.5 = 13.416

Step 4: Square Step 3.
13.416*13.416= 179.9891= 180 sample size approx

19) Step 1: Find z a/2 by dividing the confidence interval by two, and looking that area up in the z-table:

.90/2 = 0.45. The closest z-score for 0.45 is 1.645.

Step 2: Multiply step 1 by the standard deviation.
1.645 * 900 = 1480.5

Step 3: Divide Step 2 by the margin of error. Our margin of error (from the question), is 300.

1480.5/300 = 4.935

Step 4: Square Step 3.
4.935*4.935= 24.35423= 24 required sample size

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