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Sixty-four students in an introductory college economics class were asked how many credits they had earned in college, and how certain they were about their choice of major. At α = 0.05, is the degree of certainty independent of credits earned?

Credits Earned	Very Uncertain	Somewhat Certain	Very Certain	Row Total
0 – 9	13	6	5	24
10 – 59	9	4	6	19
60 or more	4	9	11	24

Col Total	26	19	22	67

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(a)

At α = .05, the hypothesis for the given issue is H₀: Credits Earned and Certainty of Major are independent.

[removed]	No
[removed]	Yes

(b)

Calculate the Chi-Square test statistic, degrees of freedom and the p-value. (Round your test statistic value to 2 decimal places and the p-value to 4 decimal places.)


Test statistic	[removed]
d.f.	[removed]
p-value	[removed]

(c)

Find the critical value of the Chi-Square for α = .05. (Round your answer to 2 decimal places.)

Critical value

[removed]

(d)

We cannot reject the null hypothesis and find dependence.

[removed]

Yes

[removed]

In a four-digit lottery, each of the four digits is supposed to have the same probability of occurrence. The table shows the frequency of occurrence of each digit for 79 consecutive daily four-digit drawings.

Digit	Frequency
0	42
1	29
2	20
3	43
4	20
5	30
6	29
7	29
8	41
9	33

Total	316

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(a)

The hypothesis for the given issue is H₀: The digits come from a uniform population.

[removed]	No
[removed]	Yes

(b)

Calculate the Chi-Square test statistic, degrees of freedom and the p-value. (Round your test statistic value to 2 decimal places and the p-value to 4 decimal places.)