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During 2019, the standard deviation of ACT scores of the students at UA was 40. A...

During 2019, the standard deviation of ACT scores of the students at UA was 40. A sample of 16 students had a standard deviation of 45. Testing to see if there has been a significant change in the standard deviation of ACT scores at UA.

a. Develop null and alternative hypotheses.

b. What is the value of test statistic?

c. At 95% confidence, what are the critical values (C.V)

d. What is the conclusion?

math   Statistics-And-Probability   
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Answer #1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: σ = 40
Alternative Hypothesis, Ha: σ ≠ 40

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (16 - 1)*45^2/40^2
Χ^2 = 18.984

This is two tailed test, for α = 0.05 and df = 15
Critical value of Χ^2 are 6.262 and 27.488

Do not reject null hypothesis
There is no significant change in the standard deviation

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