Problem 1: Women in Olympiads

The International Olympic Committee (IOC) stated that the female participation in the 2012 London Olympic Games was 46%, a remarkable increase from previous years. Broadcasting and clothing companies want to change their advertising and marketing strategies if the female participation keeps increasing at the next games in Rio. An independent sports expert arranged for a random sample of pre-Olympic exhibitions. The sports expert reported that 254 of 496 athletes in the random sample were women. The expert wants to determine if this is strong evidence at the 5% significance level to show that the women participation may increase in the next Olympic Games.

1) What type of hypothesis test is required here? Explain the requirements of this test.

2) Is this a right tailed, left tailed or two-tailed test?

3) State the null and alternate hypotheses here. H_o : H₁ :

4) Find the critical value and the test statistics. State them here.

5) Find the p-value of the test and state it here.

6) Make a statistical decision and justify it based on your findings from above.

7) Interpret this statistical decision in the context of the problem.