If the calculated chi-squared value is greater than the critical value what can

Question

If the calculated chi-squared value is greater than the critical value what can you conclude?

fail to reject the null model

reject the alternative model

reject the null model

1.    Your professor tells you that they will roll a die in order to determine how many points each question on an upcoming test will be worth. To be sure that the die they are going to use is a fair die, a sample of die rolls was take. The table below shows the results for rolls of the die.

What is the expected frequency for a result of 3? (calculate to 1 decimal)

Result

1

2

3

4

5

6

Frequency

27

26

25

18

15

20

Suppose that we have a population of fungal spores which clearly fall into two size categories, large and small. We incubate these spores on agar and count the number of spores that germinate by producing a single outgrowth or multiple outgrowths. The null hypothesis is that spore size and outgrowth are independent of each other.

What is the calculated Chi-Squared value for this set of data for significance level of 0.05? (answer to 3 decimals)

Small Spore

Large Spore

Single Outgrowth

10

14

Multiple Outgrowths

21

19

fail to reject the null model

reject the alternative model

reject the null model

Explanation / Answer

(first part) If the calculated chi-squared value is greater than the critical value what can you conclude? reject the null model

(second part) here probability of each face of die=1/6,

total observed frequency=n=131

so expected frequency for each face of die=n/6=131/6=21.8

(third part) answer is 0.705

here we find the expected frequency as given in following table and

chi-square=sum((O-E)2/E)=0.705 with (r-1)(c-1)=(2-1)*(2-1)=1 df

critical chi-square(0.05,1)=3.84 is more than calculated chi-square, so we fail to reject null hypothesis H0 that spore and outgrowth are independent

Result 1 2 3 4 5 6 total Frequency(observed) 27 26 25 18 15 20 131 Frequency(Expected) 21.8 21.8 21.8 21.8 21.8 21.8 131

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