In the United States, shoe size is normally distributed. The average shoe size for a woman is 8.5, with a standard deviation of 1.5. The average show size for men is 10, with a standard deviation of 1.5

What's your US shoe size? You can use this website for conversions: https://www.shoesinternational.co.uk/shoe-size-conversion

Find your own z-score!

1. Based on the population distribution of women's shoes, what would the z-score be for your own shoe size?

2. What is the probability of a woman having your shoe size or larger?

3. Based on the population distribution of men's shoes, what would the z-score be for your own shoe size?

4. What is the probability of a man having your shoe size or smaller?

5. What size shoe has a z-score of 2 of women's shoes?

6. What size shoe has a z-score of 2 of men's shoes?

7. If we made a sampling distribution based on the population distribution of women's shoe sizes, what would be the shape of the sampling distribution?

8. What's the minimum sample size we should use if we don't know the shape of the population distribution?

9. Using a sample of 9 women, what would the mean shoe size of the sampling distribution be?

10. Using a sample of 9 women, what would the standard error be?

11. What would be the probability of the sample having a mean of 10?

I want to know if people who run track have different sized feet than the rest of the US population. I collect a sample of 49 male track athletes who have an average shoe size of 10.5 from the US population of men.

Conduct a hypothesis test!

12. State the hypotheses symbolically.

13. If = .05, what is the critical z score?

Conduct the hypothesis test.

14. What's the z test statistic?

15. What's p value?

16. What decision should you make about the null hypothesis?

17. What is the effect size?

18. What is the probability you made a Type 1 error?