Question

In the state of California, the mean for Introduction to calculus is known to be µ=74, with s = 12.3. A certain class of 170 students had a mean of 76. You wish to know whether the class mean is statistically different from the provincial mean. Use an alpha level of 0.05 and state the critical value of z this corresponds to. Show the calculation of each component of the z value separately. Report your conclusion in a sentence that acknowledges the type of error possible.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 74
Alternative Hypothesis, Ha: μ ≠ 74

Rejection Region
This is two tailed test, for α = 0.05
Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (76 - 74)/(12.3/sqrt(170))
z = 2.12

P-value Approach
P-value = 0.034
As P-value < 0.05, reject the null hypothesis.