# Question

17.39

Perform the Durbin–Watson test at the 5% significance level to determine whether positive first-order autocorrelation exists when d = 1.10, n = 25, and k = 3.

17.42

Test the following hypotheses with α = .05.

20.19

Plot the following time series to determine which of the trend models appears to fit better.

Period 1 2 3 4 5 6 7 8 9 10

Time Series 55 57 53 49 47 39 41 33 28 20

20.35

The following trend line and seasonal indexes were computed from 4 weeks of daily observations. Forecast the 7 values for next week.

Day

Seasonal Index

Sunday 1.5

Monday .4

Tuesday .5

Wednesday .6

Thursday .7

Friday 1.4

Saturday 1.9

22.2

Draw the decision tree for Exercise 22.1.

(Exercise: 22.1) Set up the opportunity loss table from the following payoff table.

a 1 a 2

s 1 55 26

s 2 43 38

s 3 29 43

s 4 15 51

22.11

The owner of a clothing store must decide how many men’s shirts to order for the new season. For a particular type of shirt, she must order in quantities of 100 shirts. If she orders 100 shirts, her cost is $10 per shirt; if she orders 200 shirts, her cost is $9 per shirt; and if she orders 300 or more shirts, her cost is $8.50 per shirt. Her selling price for the shirt is $12, but any shirts that remain unsold at the end of the season are sold at her famous “half-price, end-of-season sale.” For the sake of simplicity, she is willing to assume that the demand for this type of shirt will be 100, 150, 200, or 250 shirts. Of course, she cannot sell more shirts than she stocks. She is also willing to assume that she will suffer no loss of goodwill among her customers if she understocks and the customers cannot buy all the shirts they want. Furthermore, she must place her order today for the entire season; she cannot wait to see how the demand is running for this type of shirt.

• a. Construct the payoff table to help the owner decide how many shirts to order.

• b. Set up the opportunity loss table.

• c. Draw the decision tree

Perform the Durbin–Watson test at the 5% significance level to determine whether positive first-order autocorrelation exists when d = 1.10, n = 25, and k = 3.

17.42

Test the following hypotheses with α = .05.

20.19

Plot the following time series to determine which of the trend models appears to fit better.

Period 1 2 3 4 5 6 7 8 9 10

Time Series 55 57 53 49 47 39 41 33 28 20

20.35

The following trend line and seasonal indexes were computed from 4 weeks of daily observations. Forecast the 7 values for next week.

Day

Seasonal Index

Sunday 1.5

Monday .4

Tuesday .5

Wednesday .6

Thursday .7

Friday 1.4

Saturday 1.9

22.2

Draw the decision tree for Exercise 22.1.

(Exercise: 22.1) Set up the opportunity loss table from the following payoff table.

a 1 a 2

s 1 55 26

s 2 43 38

s 3 29 43

s 4 15 51

22.11

The owner of a clothing store must decide how many men’s shirts to order for the new season. For a particular type of shirt, she must order in quantities of 100 shirts. If she orders 100 shirts, her cost is $10 per shirt; if she orders 200 shirts, her cost is $9 per shirt; and if she orders 300 or more shirts, her cost is $8.50 per shirt. Her selling price for the shirt is $12, but any shirts that remain unsold at the end of the season are sold at her famous “half-price, end-of-season sale.” For the sake of simplicity, she is willing to assume that the demand for this type of shirt will be 100, 150, 200, or 250 shirts. Of course, she cannot sell more shirts than she stocks. She is also willing to assume that she will suffer no loss of goodwill among her customers if she understocks and the customers cannot buy all the shirts they want. Furthermore, she must place her order today for the entire season; she cannot wait to see how the demand is running for this type of shirt.

• a. Construct the payoff table to help the owner decide how many shirts to order.

• b. Set up the opportunity loss table.

• c. Draw the decision tree

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