# Homework

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• Mar 7th 2008, 03:51 PM
Aala
Homework
8.46 A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were
3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477

(a) Construct a 90 percent confidence interval for the true mean weight.

(b) What sample size would be necessary to estimate the true weight with an error of ± 0.03 grams with 90 percent confidence?

(c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during
manufacture. (Data are from a project by MBA student Henry Scussel.)

8.62 In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 1,143 were positive.

(a) Construct a 95 percent confidence interval for the population proportion of positive drug tests.

(b) Why is the normality assumption not a problem, despite the very small value of p? (Data are from Flying 120, no. 11 [November 1993], p. 31.)
• Mar 7th 2008, 06:13 PM
mr fantastic
Quote:

Originally Posted by Aala
8.46 A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were
3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477

(a) Construct a 90 percent confidence interval for the true mean weight.

(b) What sample size would be necessary to estimate the true weight with an error of ± 0.03 grams with 90 percent confidence?

(c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during
manufacture. (Data are from a project by MBA student Henry Scussel.)

[snip]

The identical question (asked by an ostensibly different member) was asked and discussed here.

And cop this.
• Mar 7th 2008, 06:27 PM
mr fantastic
Quote:

Originally Posted by Aala
[snip]In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 1,143 were positive.

(a) Construct a 95 percent confidence interval for the population proportion of positive drug tests.

(b) Why is the normality assumption not a problem, despite the very small value of p? (Data are from Flying 120, no. 11 [November 1993], p. 31.)

(a) $\displaystyle n = 86991$.

Sample proportion: $\displaystyle \hat{\theta} = \frac{1143}{86991}$.

True proportion: $\displaystyle \theta$.

95% confidence interval: $\displaystyle \hat{\theta} - 1.96 \sqrt{\frac{\hat{\theta}(1 - \hat{\theta})}{n}} < \theta < \hat{\theta} + 1.96 \sqrt{\frac{\hat{\theta}(1 - \hat{\theta})}{n}}$.

(b) $\displaystyle n$ is large.