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.

Problem 2: Selling farm property

A statewide real estate sales agency in Ohio specializes in selling farm property. Their records indicate that the mean selling time of farm property is 95 days. Because of increasing industrialization in the state of Ohio, the agency believes that this time now is greater than 95. A statewide survey of 60 farms sold recently and selected randomly revealed that their mean selling time was 99 days, with a standard deviation 24 days. At the 0.05 significance level, conduct a hypothesis testing to determine if there has been an increase in selling time.

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.

Problem 3: Self-checkout systems

Many grocery stores and large retailers such as Walmart and Target have installed self-checkout systems so shoppers can scan their own items and cash out themselves. A Walmart in Columbus, Ohio wanted to see how well liked these self-checkouts are and how often customers use them. They randomly selected a sample of 15 days from their summer calendar and recorded the number of customers using their self-checkout registers. Below is the list of number of customers using this service during these 15 days.

120 108 119 115 118 92 118 94 106 106 112 101 120 108 95

Conduct a hypothesis test to determine whether the number of customers using the self-checkout system is different than 100 customers per day. Use a 5% significance level.

1) What type of hypothesis test is needed 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.