Assignment:
Q1: 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.
Q2: 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?
Q3: 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?
Q4: A machine used for packaging seedless golden raisins is set so that ther standard deviation in the weight of raisins packged per box is 0.25 ounce. The operations manager wishes to test the machine setting and selects a sample of 30 consecutive raisin packges filled during the production process. Their weights are as recorded on the worksheet.
| Weight |
| 15.2 |
| 15 |
| 14.3 |
| 15.3 |
| 15.2 |
| 14.4 |
| 15.1 |
| 15.4 |
| 15.5 |
| 15.7 |
| 15.6 |
| 15.4 |
| 15.3 |
| 15.7 |
| 15.2 |
| 15 |
| 15.4 |
| 15.5 |
| 15.1 |
| 15.3 |
| 15.6 |
| 14.3 |
| 14.9 |
| 15.1 |
| 14.6 |
| 14.8 |
| 15.3 |
| 14.5 |
| 14.6 |
| 15.1 |
a. At the 0.05 level of significance, is there evidence that the population standard deviation differs from 0.25 ounces?
b. What are the degrees of freedom?
c. What is the chi-statistic?
Q5: 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?
What percent of the total variation in candy bar sales is explained by prices?
Q6: 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.
| Foul Shots Made |
Number Taken |
| 73 |
100 |
|
| 75 |
100 |
|
| 69 |
100 |
|
| 72 |
100 |
|
| 77 |
100 |
|
| 71 |
100 |
|
| 68 |
100 |
|
| 70 |
100 |
|
| 67 |
100 |
|
| 74 |
100 |
|
| 75 |
100 |
|
| 72 |
100 |
|
| 70 |
100 |
|
| 74 |
100 |
|
| 73 |
100 |
|
| 76 |
100 |
|
| 69 |
100 |
|
| 68 |
100 |
|
| 72 |
100 |
|
| 70 |
100 |
|
| 64 |
100 |
|
| 67 |
100 |
|
| 72 |
100 |
|
| 70 |
100 |
|
| 74 |
100 |
|
| 76 |
100 |
|
| 75 |
100 |
|
| 78 |
100 |
|
| 76 |
100 |
|
| 80 |
100 |
|
| 78 |
100 |
|
| 83 |
100 |
|
| 84 |
100 |
|
| 81 |
100 |
|
| 86 |
100 |
|
| 85 |
100 |
|
| 86 |
100 |
|
| 87 |
100 |
|
| 85 |
100 |
|
| 85 |
100 |
|
Q7: 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 Yi = 1.2 + 0.5Xi
What is the fitted trend value for this time series on real net sales for the tenth year?