Question

1) Consider the following contingency table that records the results obtained for four samples of fixed sizes selected from four populations.

	Sample Selected From
	Population 1	Population 2	Population 3	Population 4
Row 1	34	75	102	71
Row 2	24	58	79	110
Row 3	35	47	72	10

a. calculate the expected frequencies for all cells assuming that the null hypothesis is true.

Round your answers to three decimal places, where required.

	Population 1	Population 2	Population 3	Population 4	Total
Row 1
Row 2
Row 3
Total

b. For α=0.025, find the critical value of χ2. Specify the rejection and nonrejection regions on the chi-square distribution curve.

Enter the exact answer from the chi-square distribution table.

χ2=

c. Find the value of the test statistic χ2. Round your answer to three decimal places. The value of the test statistic χ2 is .... ?

2) Bob’s Pest Removal Service specializes in removing wild creatures (skunks, bats, reptiles, etc.) from private homes. He charges $74 to go to a house plus $23per hour for his services. Let y be the total amount (in dollars) paid by a household using Bob’s services and x the number of hours Bob spends capturing and removing the animal(s). The equation for the relationship between x and y is y=23x+74.

a. Bob spent 3 hours removing a coyote from under Alice’s house. How much will he be paid?

3) A researcher took a sample of 1010 years and found the following relationship between x and y, where x is the number of major natural calamities (such as tornadoes, hurricanes, earthquakes, floods, etc.) that occurred during a year and y represents the average annual total profits (in millions of dollars) of a sample of insurance companies in the United States.

^y =337.0−2.0x (For this question, the ^y should show the arrow above the y, I don't know the name of the symbol)

Answer 1

1. a)

Observed Frequencies
	Population 1	Population 2	Population 3	Population 4	Total
Row 1	34	75	102	71	282
Row 2	24	58	79	110	271
Row 3	35	47	72	10	164
Total	93	180	253	191	717
Expected Frequencies
	Population 1	Population 2	Population 3	Population 4	Total
Row 1	93 * 282 / 717 = 36.5774	180 * 282 / 717 = 70.795	253 * 282 / 717 = 99.5063	191 * 282 / 717 = 75.1213	282
Row 2	93 * 271 / 717 = 35.1506	180 * 271 / 717 = 68.0335	253 * 271 / 717 = 95.6248	191 * 271 / 717 = 72.1911	271
Row 3	93 * 164 / 717 = 21.272	180 * 164 / 717 = 41.1715	253 * 164 / 717 = 57.8689	191 * 164 / 717 = 43.6876	164
Total	93	180	253	191	717
	(fo-fe)²/fe
Row 1	(34 - 36.5774)²/36.5774 = 0.1816	(75 - 70.795)²/70.795 = 0.2498	(102 - 99.5063)²/99.5063 = 0.0625	(71 - 75.1213)²/75.1213 = 0.2261
Row 2	(24 - 35.1506)²/35.1506 = 3.5372	(58 - 68.0335)²/68.0335 = 1.4797	(79 - 95.6248)²/95.6248 = 2.8903	(110 - 72.1911)²/72.1911 = 19.8018
Row 3	(35 - 21.272)²/21.272 = 8.8595	(47 - 41.1715)²/41.1715 = 0.8251	(72 - 57.8689)²/57.8689 = 3.4507	(10 - 43.6876)²/43.6876 = 25.9766

b) df = (r-1)(c-1) = 6

Critical value:

χ²α = CHISQ.INV.RT(0.025, 6) = 14.449

c) Test statistic:

χ² = ∑ ((fo-fe)²/fe) = 67.541

Decision:

As χ² > 14.449, Reject Ho.

-----------

2. ŷ = 74 + (23) x

Predicted value of y at x = 3

ŷ = 74 + (23) * 3 = $ 143

------

3, It is incomplete question.