# Applied Statistical Tools

A sample of size 25 provides a sample variance of 400. The standard error, in this case equal to 4, is best described as the estimate of the standard deviation of means calculated from samples of size 25.

Blossom's Flowers purchases roses for sale for Valentine's Day. The roses are purchased for $10 a dozen and are sold for $20 a dozen. Any roses not sold on Valentine's Day can be sold for $5 per dozen. The owner will purchase 1 of 3 amounts of roses for Valentine's Day: 100, 200, or 400Â dozen roses. The number of alternatives for the payoff table is

2

3

4

The data below represents the amount of grams of carbohydrates in a sample serving of breakfast cereal.

10 18 24 30 19 22 24 20 18 25 20 22 19

The coefficient of variation for this data would be __________%.

Answer should be consistent with examples in your Levine et al. text and be between one or two decimal places e.g. 12.3 or 12.34 etc.

Please do NOT include units (%) in your answer.

The manager of a service station is in the process of analyzing the number of times car owners change the oil in their cars. She believes that the average motorist changes his or her car's oil less frequently than recommended by the owner's manual (two times per year). In a preliminary survey she asked 15 car owners how many times they changed their car's oil in the last 12Â months. The results are listed below.

1 1 2 1 2

2 0 1 0 1

2 3 1 3 0

QUESTION 18

The value of the test statistic in this problem is approximately equal to __________?

Answer should be between two and four decimal places e.g. 1.23, 1.234, 1.2345 etc.

Please do NOT include any units in your answer.

What would be your decision if a hypothesis test was conducted on this problem with the null hypothesis given as H0 : µ ≥ 2 and the alternate hypothesis given as H1 < 2.

Reject H0 at the 10%, 5% and 1% level of significance

Reject H0 at the 10% and 5% level of significance but do not reject H0 at the 1% level of significance

Reject H0 at the 10% level of significance but do not reject H0 at the 5% or 1% level of significance

Do not reject H0 at either the 10%, 5% or 1% level of significance.

The following information refers to the next two questions:

Refer to the following table which contains the sales (in $,000) for a department store for the first ten months of the year.

Month Sales

January 440

February 480

March 590

April 400

May 500

June 550

July 470

August 500

September 600

October 520

Using a three period moving average (i.e. MA(3)) as a forecasting method, what is the MSE for this forecasting model?

Answer should be between two and four decimal places e.g. 1.23, 1.234, 1.2345 etc.

Please do NOT include any units in your answer.

Using simple exponential smoothing (with a smoothing constant of 0.2) as a forecasting method, what is the MAPE for this forecast model __________%

Answer should be consistent with examples in your study material and be between one or two decimal places e.g. 0.12, 0.123 etc.

Please do NOT include units (%) in your answer.

The following information refers to the next question:

The ordered array below resulted from taking a sample of 25 batches of 500 computer chips and determining how many in each batch were defective.

Defects

1 2 4 4 5 5 6 7 9 10 12 12 14

17 20 21 23 23 24 26 27 27 28 29 29

If a frequency distribution for the defects data is constructed, using '0 but less than 5' as the first class, what would be the cumulative relative frequency of the '10 but less than 15' class __________%

Answer should be a percentage value to whole numbers e.g. 12, 23, 34 etc.

Please do NOT include units (%) in your answer.

The following information refers to the next question:

A manufacturer of power tools claims that the average amount of time required to assemble their top-of-the-line table saw is fifty (50) minutes with a standard deviation of forty (40) minutes (the very large standard deviation is due to a variety of factors including a large variation in skills amongst the 'Do it yourself' home handyman which is traditionally one of the companies customer base). Suppose a random sample of 64 purchasers of this table saw is taken.

QUESTION 23

What is the probability that the sample mean will be less than 46 minutes __________?

Answer should be to four decimal places which is consistent with the number of decimal places listed in your appendix tables e.g. 0.1234 etc.

Please do NOT include any units in your answer.

The following information refers to the next question:

A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. The desired length of the insulation is 12 metres. It is known that the standard deviation in the cutting length is 0.15 metres. A sample of 144 cut sheets yield a mean length of 12.14 metres. This sample will be used to obtain a 95% confidence interval for the mean length cut by machine.

QUESTION 24

What are the two limits of the confidence interval __________ and __________?

Answer should be to four decimal places e.g. 1.2345 and 2.3456.

Please do NOT include any units in your answer.

min =

max =

The following information refers to the next four questions:

An insurance company wishes to examine the relationship between income (in $,000) and the amount of life insurance (in $,000) held by families. The company drew a simple random sample of families and obtained the following results:

Family Income Amount of life insurance

A 40 110

B 80 200

C 110 220

D 80 150

E 80 170

F 120 270

G 60 140

H 100 240

I 60 150

J 90 200

What is the least squares estimate of the slope?

Answer should be to four decimal places e.g. 1.2345.

Please do NOT include any units in your answer.

What is the least squares estimate of the Y intercept?

Answer should be to four decimal places e.g. 1.2345.

Please do NOT include any units in your answer.

What is the prediction for the amount of life insurance for a family whose income is $85,000?

Answer should be to four decimal places e.g. 1.2345.

Please do NOT include any units in your answer.

What would be the residual (error) term for a family income of $90,000?

Answer should be to four decimal places e.g. 1.2345.

Please do NOT include any units in your answer.

#### Solution Summary

The solution discusses several applied statistical tools like Regression analysis, Testing of hypothesis, Confidence interval, Normal probability rules and Forecasting using moving average and simple exponential smoothing.