The national average on a certification exam in the US last year was 68.

The national average on a certification exam in the US last year was 68. For a sample of participants (n=64) who participated in a preparatory program before the exam, the mean was 76 with a sample standard deviation of 4. Using alpha = .05, is there a statistically significant difference between the study participants’ mean and the national average?

Solutions

Expert Solution

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 68
Alternative Hypothesis, Ha: μ ≠ 68

Rejection Region
This is two tailed test, for α = 0.05 and df = 63
Critical value of t are -1.998 and 1.998.
Hence reject H0 if t < -1.998 or t > 1.998

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (76 - 68)/(4/sqrt(64))
t = 16

P-value Approach
P-value = 0
As P-value < 0.05, reject the null hypothesis.

orchestra answered 1 year ago

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