## 9.2 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' . 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. 9.1 (jamovi) and Fig. 9.2 (SPSS). We would like to test the company's claim, and ask the RQ:

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 distribution 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 Teaching Week 7 tutorial.)
11. Is it reasonable to assume the statistical validity conditions are satisfied? (Fig. 9.3 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.

### References

Dunn PK. Assessing claims made by a pizza chain. Journal of Statistical Education [Internet]. 2012;20(1). Available from: www.amstat.org/publications/jse/v20n1/dunn.pdf.