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# Statistics

Please show the work only where its necessary on a separate file.

The international Olympic Committee states that the female population in the 2000 Summer Olympic games was 42%, even with the new sports added to the Games. Sponsoring companies want to change their advertising and marketing plans if the female participation increases at the next games. An independent expert conducted a random sample of some pre-Olympic exhibitions and reported that 202 of 454 of the athletes in this random sample were women. Is this strong evidence that the participation rate may increase?

1. State the appropriate hypothesis

2. Verify your choice of models

3. What is the standard deviation of this sample proportion?

4. State your model and parameters.

5. Find P(p-hat>sample proportion for women)

7. Explain what your P-value means in this context.

Estimating a Population: A surveyor randomly selects 350 registered voters and asks if they support a proposed bill. A total of 293 voters said yes.
8. Verify the conditions

9. Find the sample proportion

10. Find a 95% confidence interval and state your findings.

11. Find a 99% confidence interval and state your findings.

A reporter made the claim that at least 80% of teenagers in the city went to the mall at least once per week. A researcher wants to check that claim and randomly surveys 437 teenagers in the city. She finds that of the teenagers surveyed, 316 go to the mall at least once per week.

13. Find the 95% confidence interval for the true proportion of teens that go to the mall at least once per week.

14. Comment on the Reporter's claim.

15. With a margin of error of no more than 2%, a surveyor want to estimate, with a 95% confidence interval, the percentage of citizens in a city that support building a new bridge. How many citizens must be surveyed?

16. Suppose previous polls suggest that 22% of the citizens support building a new bridge. How many citizens must be surveyed?

Two Proportions: In a company 138 of 1,562 women and 75 of 1041 men did not receive a yearly raise. Test the claim that a greater proportion of women did not receive a raise using alpha = 0.05.

17. Sate the null and alternate hypothesis

18. Calculate all three proportions.

19. Calculate Z.

20. Calculate the critical value.

22. Calculate the P-value. What is the value and how does it (or doesn't it) support your decision?

In a random sample of 150 men and 150 women at the above company, 82% of the men and 88% of the women said they were satisfied with their jobs. Using an alpha of 0.1, Is there enough evidence to suggest that the proportions are significantly different?

24. Find both the values of the number of women satisfied and the number of men satisfied with their jobs.

25. Calculate the P-value.

27. You are up for your annual job performance review. You estimate that there's a 30% chance you'll get a promotion, a 40% chance of a raise and a 20% chance of getting both a raise and a promotion. Find the probability that you get a raise or promotion.

28. Given the above conditions, are the raise and the promotion independent events? Explain!!!

29. Which of these events has a geometric model?
A. The number of black cards in a 10-card hand
B. the color of the cars in the parking garage
C. the number of hits a baseball player gets in 6 times at bat
D. the number of cards drawn from a deck until we find four aces
E. the number of people we survey until we find someone that owns an iPad

30. Which of the above choices is most likely to have a binomial model?
A. black cards?
B. car colors
C. hits at bat
D. looking for aces