STAT177 Homework sheet #3 Solutions

1) We choose normal from the probability distributions menu on Gerry’s stats tools. The value of x is 35, the mean is 30, the standard deviation is 12.5, the sample size box is blank, and the radio button is less than. The dialogue box gives the answer 65.54%.

2) Same as 1, except the value of x is 50 and the radio button is greater than. The dialogue box gives the answer 5.48%

3) We choose normal percentiles from the probability distributions menu on Gerry’s stats tools. The percentile wanted is 0.9, the mean is 30, and the standard deviation is 12.5. The dialogue box gives the answer 46.0194 which we round to 46.02.

4) We need the 2.5^th and 97.5^th percentiles. For the first, the percentile wanted is 0.025 which gives the value of 5.5005 which rounds to 5.50; for the second, the percentile wanted is 0.975 which gives the value of 54.4995 which rounds to 54.50.

5) We choose normal from the probability distributions menu on Gerry’s stats tools. The value of x is 25, the mean is 30, the standard deviation is 12.5, the sample size is 50, and the radio button is less than. The dialogue box gives the answer 0.23%.

6) We choose normal from the probability distributions menu on Gerry’s stats tools. The thing to recognize is that P(74.7 < X < 75.3) = P(X < 75.3) – P(X < 74.7). For P(X < 75.3), the value of x is 75.3, the mean is 75, the standard deviation is 1.2, the sample size is 60, and the radio button is less than. The dialogue box gives the answer 97.36%. For P(X < 74.7), the value of x is 74.7; the dialogue box gives the answer 2.64%. The final answer is 97.36% - 2.64% = 94.72%

7) Ho: m £ 1000

Ha: m > 1000

8) Since the p-value is less than the level of significance, we reject the null hypothesis. We conclude the average is greater than $1000 and thus that the campaign was successful.

9) Under this scenario, the p-value would be greater than the level of significance and we would reach the opposite conclusion that the campaign was not successful.

10) Ho: m ³ 1

Ha: m < 1

11) Since the p-value is less than 1%, under the general rule of thumb, we would reject the null hypothesis and conclude that the training was successful.

12) In theory, a Type I error could have been committed. Since we used the general rule of thumb, the maximum probability of a Type I error would be 1%.

13) Ho: m = 2 L

Ha: m ¹ 2L

14) Since the p-value is greater than the level of significance, we do not reject the null hypothesis and conclude the standards are being maintained.

15) Since the p-value is greater than 10%, under the general rule of thumb, we would not reject the null hypothesis and reach the same conclusion.