Question

An internet-based organization that allows individuals and groups to raise funds for a project. In April 2020, the mean total for pledges per project, m, was $3165.00 US dollars.

A random sample of 14 projects from April 2020 has the following characteristics:

            n = 14

            `X = $2459.30

            s = $887.62

All of the projects were in the category “Comics.”

(a) Specify the hypotheses for a t-test to determine whether the mean funding per project for “Comics” projects is lower than the overall mean for April 2020. Use a one-sample t-test with a = 0.05. Assume that the sample data are more or less normally distributed.

(b) Conduct a hypothesis test with a = 0.05, estimating the t-statistic and the p-value.

(c) Report:

the level of significance,

            the type and value of the test statistic (including degrees of freedom if appropriate),

            the p-value (exact values if possible, or a range of possible values), and

            the implications for the null hypothesis.

What do the results of the hypothesis test tell us about the difference between the mean for the “Comics” category and the mean for all types of projects, m = $3165.00 US dollars?

(d) Compute and interpret a 95% confidence interval for the population mean of the “Comics” category. Does the confidence interval include the population mean for all projects, m = $3165.00 US dollars? What does this imply about the funds raised for a typical “Comics” project compared to the mean for all types of projects?

Answer 1