# Tootsie Rolls & Pre-employment Drug Tests

Please complete the following and note that methods of computation could include the usage of Excel.

1. 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.) Tootsie

2. 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.)

© BrainMass Inc. brainmass.com June 3, 2020, 10:06 pm ad1c9bdddfhttps://brainmass.com/business/business-math/statistics-random-sample-of-tootsie-rolls-faa-pre-employment-drug-tests-215095

#### Solution Preview

Please find the solution in the attached file.

Solution-1

(a) Sample mean = ( 3.087 + 3.131 + 3.241+ 3.241+ 3.270 + 3.353 + 3.400 + 3.411 + 3.437

+ 3.477)/10 = 3.3048

Standard deviation = 0.132

Confidence Interval =

...

#### Solution Summary

Confidence intervals are constructed, sample sizes chosen and factors discussed in these statistic questions.