# Stats Answers

1. A sample of the longest running shows on Broadway shows they had runs lasting the following number of years. Calculate the mean, median, mode, range, variance, and standard deviation in years.

9 4 4 13 7 6 3

2. Construct a frequency distribution and a frequency histogram of the following data:

Commuting Distance (One-Way) for Thirty-Two Workers (Miles)

13 7 10 3 15 40 11 8

4 62 15 31 17 26 8 19

10 3 21 1 16 28 24 17

12 6 19 28 35 11 16 21

3. Construct the 90%and 99% confidence interval for the population mean of the following data. Which is wider?

A computer manufacturer wants to estimate the mean number of hours per day all adults use computers at home. In a random sample of 21 adults, the mean length of time a computer was used at home was 1.7 hours. From past studies the company assumes sigma is 0.6 hour and that the population of times is normally distributed.

4. The proportion of middle managers leaving large IT companies within three years is to be estimated within 3 percent. The 0.95 degree of confidence is to be used. A study conducted several years ago revealed that the percent of managers leaving within three years was 21. To update this study, how many managers' files should be analyzed?

A. 511

B. 623

C. 709

D. 895

5. Tax Cuts or Entitlements? An economist believes that the distribution of opinions of US adults about whether tax cuts or entitlements is more important is different than the following:

Favor Percentage

Entitlements 77%

Tax Cuts 15%

Unsure 8%

TOTAL 100%

The economist conducts a survey. She randomly selects 600 adults and asks "which is more important, keeping Medicare, Social Security and Medicaid (entitlements) or tax cuts". The results follow: At alpha= 0.01, are the distributions different?

Survey Results

Response Frequency.f

Keeping Medicare, Social Security, and Medicaid 431

Tax Cuts 107

Unsure 62

TOTAL 600

6. A researcher wants to determine if a relationship exists between job status (full- or part-time) and two different work arrangements - contract and traditional. The results of a random sample of 884 workers are shown in the following contingency table: Can the researcher use this sample to test for independence using a Chi-Square independence test? Why or why not?

Work Arrangement

Status Contract Traditional

Full-time 12 720

Part-time 4 148

7. A travel consultant wants to determine whether certain desirable travel features are related to the travel purpose. A random sample of 300 travelers is selected and each is asked for their primary travel feature. The results are shown in the contingency table below. Assuming that the variables travel feature and travel purpose are independent, find the expected frequency for each cell.

a. Calculate the marginal (row and column) frequencies.

b. Determine the sample size.

c. Use the appropriate formula to find the expected frequency for each cell.

Travel Feature

Travel Purpose Hotel Rooms Leg Room on Planes Rental Car Size Other

Business 36 108 14 22

Leisure 38 54 14 14

8. An HR manager is concerned about absenteeism. She decides to sample the records to determine if absenteeism is distributed evenly throughout the six-day workweek. The null hypothesis to be tested is: Absenteeism is distributed evenly throughout the week. The 0.01 level is to be used. The sample results are:

What is the calculated value of chi-square?

#### Solution Preview

1. A sample of the longest running shows on Broadway shows they had runs lasting the following number of years. Calculate the mean, median, mode, range, variance, and standard deviation in years.

9 4 4 13 7 6 3

Answers

X X - X̅ (X - X̅)^2

9 2.428571429 5.897959186

4 -2.571428571 6.612244896

4 -2.571428571 6.612244896

13 6.428571429 41.32653062

7 0.428571429 0.18367347

6 -0.571428571 0.326530612

3 -3.571428571 12.75510204

46 73.71428571

Mean = = 6.571428571 years

Median = item when the items are arranged in ascending or descending order of magnitude.

= item = 4th item = 6 years

Mode = most frequently occurring item

= 4 years

Range = Highest observed value - Lowest observed value

= 13 - 3

= 10 years

Sample variance = = 12.28571429 years

Sample standard deviation = = 3.505098328 years

2. Construct a frequency distribution and a frequency histogram of the following data:

Commuting Distance (One-Way) for Thirty-Two Workers (Miles)

13 7 10 3 15 40 11 8

4 62 15 31 17 26 8 19

10 3 21 1 16 28 24 17

12 6 19 28 35 11 16 21

Answers

Commuting Distance

lower upper midpoint width frequency

0 < 10 5 10 8

10 < 20 15 10 14

20 < 30 25 10 6

30 < 40 35 10 2

40 < 50 45 10 1

50 < 60 55 10 0

60 < 70 65 10 1

32

3. Construct the 90%and 99% confidence interval for the population mean of the following data. Which is wider?

A computer manufacturer wants to estimate the mean number of hours per day all adults use computers at home. In a random sample of 21 adults, the mean length of time a computer was used at home was 1.7 hours. From past studies the company assumes sigma is 0.6 hour and that the population of times is normally distributed.

Answers

90% confidence interval

The confidence interval is given by , where = 1.7, σ = 0.6, n = 21, = 1.644853627

That is,

= (1.48, 1.92)

Thus with 90% confidence we can claim that population mean number of hours per day all adults use computers at home is within (1.48, 1.92) hours.

Details

Confidence Interval Estimate for the Mean

Data

Population Standard Deviation 0.6

Sample Mean 1.7

Sample Size 21

Confidence Level 90%

Intermediate Calculations

Standard Error of the ...

#### Solution Summary

The solution provides step by step method for the calculation of descriptive statistics, confidence interval and hypothesis testing. Formula for the calculation and interpretation of results are also provided.