In: Statistics and Probability
As a researcher, you are curious if people who eat vitamins have more energy. To assess this question, you will calculate a confidence interval for the following data. The average energy on a scale of 1-20 in the general population is μ (mu) = 13, with σ (sigma) = 3.5. You recruit 36 people who eat vitamins and assess their energy. This sample has an average of xbar = 14.
a. State the null and alternative hypotheses.
b. Find the corresponding critical z-value for Type I error rate (alpha) of α = 0.05.
c. What level of confidence do you have?
d. Please calculate the confidence interval for these data.
e. Would you retain or reject the null hypothesis? Explain your answer based on the confidence interval.
f. In everyday language, what do these results tell you about the research question?