Question

5. In a first grade class, 9 of 24 students drink white milk with their lunch. Find the 92% confidence interval for students drinking milk.

6. In an elementary school, 7 of 100 students have a peanut allergy. Find the 95% confidence interval for peanut allergies in elementary school districts.

7. The Bears have won an average of 7 games per year from 2010 to 2017 with a population standard deviation of 2.7255. For n = 16, find a 96% confidence interval for the number of wins in the 2018 season.

8. The Chicago Cubs have won an average of 83 games per year from 2008 to 2018 with a sample standard deviation of 14.4844. For n = 162, find the 98% confidence interval for the number of wins in the 2019 season.

9. The average number of hurricanes along the Atlantic coast is 6 with a population standard deviation of 2 per year. For n = 20, find the 95% confidence interval for the number of hurricanes striking the Atlantic coast per year.

10. The average snowfall at O’Hare Airport is 37.1 inches with a sample standard deviation of 5.3. For n = 10, find the 90% confidence interval for the amount of snow anticipated for the winter of 2018 to 2019.

Answer 1

In a first grade class, 9 of 24 students drink white milk with their lunch. Find the 92% confidence interval for students drinking milk.

We need to construct the 92% confidence interval for the population proportion. We have been provided with the following information about the number of favorable cases: Favorable Cases X = 9 Sample Size N = 24 The sample proportion is computed as follows, based on the sample size N = 24 and the number of favorable cases X = 9: = X N 9 24 = 0.375 The critical value for a = 0.08 is ze = 21-a/2 = 1.751. The corresponding confidence interval is computed as shown below: p(1 - i) CI(Proportion) p(1-P) • ô t ze = P ZcV n n 0.375 1.751 x 0.375(1 – 0.375) ,0.375 +1.751 x 24 0.375(1 – 0.375) 24 (0.202,0.548) Therefore, based on the data provided, the 92% confidence interval for the population proportion is 0.202 < p < 0.548, which indicates that we are 92% confident that the true population proportion pis contained by the interval (0.202,0.548).

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