Question

1. In a randomly selected sample of 200 students, 112 received grades higher than a B-. At a 10% significance level, does the sample provide enough statistical evidence to support a claim that more than 50% of all students received grades better than B-? Perform a 1 sample Z-test of proportion to analyze the sample data. A. State the null and alternative hypotheses – clearly indicate which is the null and which is the alternative. Use the symbol π to represent the population proportion in your hypotheses. B. Look up the Z critical value for this test and write out the decision rule using it. C. Calculate the sample proportion (p) AND the sample Z statistic for this test. Show all your work – no marks will be awarded without supporting calculations. D. Report the sample p-value. You do not need to show any work. E. In a full sentence answer: state whether or not you have rejected the null hypothesis AND respond to the original question (does the sample provide enough statistical evidence to support a claim that more than 50% of all students received grades better than B-?)

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: pi = 0.5
Alternative Hypothesis, Ha: pi > 0.5

b)

Rejection Region
This is right tailed test, for α = 0.1
Critical value of z is 1.28.
Hence reject H0 if z > 1.28

c)

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.56 - 0.5)/sqrt(0.5*(1-0.5)/200)
z = 1.7

d)

P-value Approach
P-value = 0.0446
As P-value < 0.1, reject the null hypothesis.

E)
yes, it provide enough statistical evidence to support a claim that more than 50% of all students received grades better than B