8.1 Hypothesis tests for one mean

In 2011, Eagle Boys’ Pizza ran a campaign that claimed that Eagle Boys’ pizzas were ‘Real size 12-inch large pizzas’ (Dunn 2012). Eagle Boys’ made the data from the campaign publicly available.

A summary of the diameters of a sample of 125 of their large pizzas is shown in Fig. 8.1 (jamovi) and Fig. 8.2 (SPSS).

Summary statistics for the diameter of Eagle Boys' large pizzas; jamovi

FIGURE 8.1: Summary statistics for the diameter of Eagle Boys’ large pizzas; jamovi

Summary statistics for the diameter of Eagle Boys' large pizzas; SPSS, slightly edited

FIGURE 8.2: Summary statistics for the diameter of Eagle Boys’ large pizzas; SPSS, slightly edited

We would like to test the company’s claim:

For Eagle Boys’ pizzas, is mean diameter actually 12 inches, or not?

  1. What is the parameter of interest?
  2. Write down the values of \(\bar{x}\) and \(s\).
  3. Determine the value of the standard error of the mean.
  4. Explain the difference in meaning between \(s\) and \(\text{s.e.}(\bar{x})\) in this context.
  5. Write the hypotheses to test if the mean pizza diameter is 12 inches.
  6. Is the alternative hypothesis one- or two-tailed? Why?
  7. Draw the normal that shows how the sample mean pizza diameter would vary by chance, even if the population mean diameter was 12 inches.
  8. Compute the \(t\)-score for testing the hypotheses.
  9. What is the approximate \(P\)-value using the 68–95–99.7 rule?
  10. Write a conclusion. (The CI was found in the Lecture 7 tutorial.)
  11. Is it reasonable to assume the statistical validity conditions are satisfied? (Fig. 8.3 may, or may not, help.)
  12. Do you think that the pizzas do have a mean diameter of 12 inches in the population, as Eagle Boys’ claim? Explain.
Histogram for the diameter of Eagle Boys' large pizzas

FIGURE 8.3: Histogram for the diameter of Eagle Boys’ large pizzas

References

Dunn, Peter K. 2012. “Assessing Claims Made by a Pizza Chain.” Journal of Statistical Education 20 (1). www.amstat.org/publications/jse/v20n1/dunn.pdf.