Question

In the province of Ontario, the mean for Introduction to Statistics is known to be µ=73, with standard deviation = 14.3. A certain class of 169 students had a mean of 75. 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

solution:

Given data:

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 73
Alternative Hypothesis, Ha: μ ≠ 73

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 = (75 - 73)/(14/sqrt(169))
z = 1.86

P-value Approach
P-value = 0.0629
As P-value >= 0.05, fail to reject null hypothesis.

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