Question

2. The average number of cups of coffee drunk each day by a randomly selected sample of 25 students was 4.4. Assume the population standard deviation is 0.5 cups of coffee. Does the sample provide enough statistical evidence to support a claim that students drink 4 cups of coffee per day on average? Test the hypothesis at a 1% level of significance. Perform a 1-sample Z-test of mean to assess the sample evidence. A. State the null and alternative hypotheses – clearly indicate which is the null and which is the alternative. Use the symbol μ to represent the population mean 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 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 students drink 4 cups of coffee per day on average?)

Answer 1

a)
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 4
Alternative Hypothesis, Ha: μ > 4

b)

Rejection Region
This is right tailed test, for α = 0.01
Critical value of z is 2.326.
Hence reject H0 if z > 2.326

c)

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (4.4 - 4)/(0.5/sqrt(25))
z = 4

d)

P-value Approach
P-value = 0
As P-value < 0.01, reject the null hypothesis.

e)

yes, sample provide enough statistical evidence to support a claim that students drink 4 cups of coffee per day on average