Most dermatologists recommend using sunscreens that have a sun protection factor (SPF) of at least 30. One of the authors wanted to find out whether the SPF of sunscreens used by students at her school (which is in a very sunny part of the U. S.) exceeds this value, on average? To collect data, the author surveyed students in her Introductory Statistics course and found that in a sample of 48 students the average SPF was 35.292 and the standard deviation of SPF was 17.186.

1.)What is the value of the statistic that you can use to summarize the data collected in the study? What notation should be used to represent it?

2.)

If we assume the population mean SPF of sunscreen used by students at this school is 30, is it possible that we could observe the statistic we did from this sample of 48 students? Why?

3.)Explain how you could use cards to, by hand, simulate one sample which assumes the null hypothesis is true. Include what you would write on the cards, what you would do with the cards, and what you would plot from the sample on the null distribution.

4. Write a conclusion in the context of the problem.