A certain county park was surveyed for plant species ten years ago. At that time

Question

A certain county park was surveyed for plant species ten years ago. At that time there were 40% Smilax, 10% Scotch Broom, 30% Toyon and 20% Poison Oak. Recently, to determine if the distribution of plant species was the same, a sample of 600 plants was taken with the following results. Use a 2% level of significance. Answer questions I through 3. This is a _____ Goodness of Fit problem Test of Independence The degrees of freedom are 5 4 3 2 The distribution of species = has changed has not changed Data from a random sample of 1000 new car buyers produced the following contingency table. Determine if Car Size and Manufacturer are independent. Use the contingency table to answer questions 4 through 5. Chi-squared = 34.67 45.81 55.87 63.72 5. Car Size and Manufacturer are independent True False The marketing manager from Dealer Don's stores wants to know if serving food samples has an effect on the sales of food or are sales independent of whether or not the store gives out food samples. 55 Dealer Don's stores are randomly selected and randomly assigned to cither give food samples or not to give food samples. Use a level of significance of 5%. Use the contingency table to answer questions 6 through 7. Chi-squared = 12.43 13.35 14.26 15.35 Giving food samples and Daily Sales are independent True False

Explanation / Answer

1. Correct answer: Option (a) Goodness of Fit

2. Correct Answer: Option (c) Degrees of freedom n-1 = 3-1 = 2

3. Correct Answer: opitinon( a) has changed

Critical X^2: 7.814736
P-Value: 0.0001

Here P-value < alpha 0.05, we reject H0

Thsu, the specie has changed

4. Correct Answer: Option (b)

The expected frequencies are calculated as

The chisquare test statistic is calculated as

Degrees of freedom: 6

Test Statistic, X^2: 45.8125
Critical X^2: 12.59157
P-Value: 0.0000

5. Correct Answer: Option (B) not independent

6.Correct Answer: Option (B)

The expected frequencies are calculated as

The chisquare test statistic is calculated as

degrees of freedom: 2

Test Statistic, X^2: 13.352
Critical X^2: 5.991471
P-Value: 0.0013

7. Correct Answer: Option (B) not independent

Oi Prob Ei (oi-Ei)^2/Ei 200 0.4 240 6.66666667 80 0.1 60 6.66666667 170 0.3 180 0.55555556 150 0.2 120 7.5 Total 21.3888889

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