# Hypothesis testing, Sample size, Confidence interval problem

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Interval Lower Limit Points

1 A random sample of 35 days taken at a large hospital shows that an average of 44 patients was treated in the emergency room per day. The standard deviation of the population is 6. Find the 99% confidence interval of the mean number of ER patients treated each day at the hospital. 0.0000 10

Interval Upper limit

0.0000 10

2 Using the same information as in question 1 above, if the director wishes to estimate the mean number of admissions per 24-hour period to within 1 admission with 99% reliability, what size sample should she choose? 0 20

3 Outline the 5 step p method in hypothesis testing.

20

The production line that packages boxes of raisins at a snack food manufacturer will be considered operating properly if the average weight of the boxes of raisin is 3.5 ounces with a standard deviation of 0.3 ounces. A random sample of 20 boxes showed an average weight of 3.30 ounces. Answer questions 4 and 5 based upon this information.

4 Provide the null and alternative hypothesis to determine if the production line is operating properly.

10

What additional assumption is needed before we can perform a test to determine whether the production line is operating properly?

10

Upper limit Points

5 State the value of the correct rejection region for alpha = 0.05. 0.0000 4

Lower Limit

0.0000 4

Upper limit

State the value of the correct rejection region for alpha = 0.01. 0.0000 4

Lower Limit

0.0000 4

What should be the correct decision and conclusion when testing to determine if the production line is operating properly by allowing a 10% probability of committing a Type 1 error? 0.0000 4

6 A machine used for packaging seedless golden raisins is set so that there standard deviation in the weight of raisins packed per box is 0.25 ounce. The operations manager wishes to test the machine setting and selects a sample of 30 consecutive raisin packages filled during the production process. Their weights are as recorded on the worksheet.

a. At the 0.05 level of significance, is there evidence that the population standard deviation differs from 0.25 ounces? 0.0000 5

b. What assumptions are made in order to perform this test?

c. What are the degrees of freedom? 0.0000 5

d) What is the chi-statistic? 0.0000 5

7 A candy bar manufacturer is interested in trying to estimate how sales are influenced by the price of their product. To do this, the company randomly chooses 6 small cities and offers the candy bar at different prices. Using candy bar sales as the dependent variable, the company will conduct a simple linear regression on the data below:

City Price ($) Sales

River Falls 1.3 100

Hudson 1.6 90

Ellisworth 1.8 90

Prescott 2 40

Rock Elm 2.4 38

Stillwater 2.9 32

What is the estimated average change in the sales of the candy bar if price goes up $1.00? 0.0000 10

What percent of the total variation in candy bar sales is explained by prices? 0.0000 10

8 A professional basketball player has embarked on a program to study his ability to shoot foul shots. On each day in which a game is not scheduled, he intends to shoot 100 foul shots. He maintains records over a period of 40 days of practice, with the results stored on the worksheet.

a. Construct a p chart for the proportion of successful foul shoots. 10

Insert p chart here.

b) Do you think that the player's fould shooting process is in statistical control? Why or why not?

10

9 "The linear trend forecasting equation for an annual time series containing 40 observations (from 1963 to 2002) on real net sales (in billions of constant 1995 dollars) is Ŷi = 1.2 + 0.5Xi

"

What is the fitted trend value for this time series on real net sales for the tenth year? 0.0000 20

10 With regards to quality and productivity management, what is the difference between common cause variation and special cause variation?

20

Total Points 200

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