**ECO351 Business Analytics II 6/1/21**

**Homework 1 (due Wed, June 9 at midnight)**

- Use at least four decimal places in your calculations. Two decimal places will be fine for z-scores.
- You can (a) submit a scanned version of your answers (there are free scanner apps which you can use for this) or (b) take good quality pictures of your work and submit those so I can easily read and grade.
- The submission folder is Homework 1 on D2L-Assessments-Assignments. If you make multiple submissions, I will grade the latest one, unless told otherwise. Please do not send your work by email.

*α = 0.01: The critical z-score for a left tail test is −2.33, for a right tail test is 2.33 and the critical z-scores for a two tail test are −2.575 and 2.575.*

*α = 0.05: The critical z-score for a left tail test is −1.645, for a right tail test is 1.645 and the critical z-scores for a two tail test are −1.96 and 1.96.*

*α = 0.10: The critical z-score for a left tail test is −1.28, for a right tail test is 1.28 and the critical z-scores for a two tail test are −1.645 and 1.645.*

- The Bureau of Census reported in 2018 that the average number of athletes in U.S. Colleges is 500. From a sample of 64 PA colleges, it is found that the sample mean of the number of athletes () is 520 in 2020. The population standard deviation is 80.

- Write the null and the alternative hypotheses to determine whether the true average number of athletes has increased since 2018.

- What is the z-score and what is your conclusion at α=0.01? Use the critical score approach to make a conclusion. Do you have enough evidence to conclude that the average number of athletes increased?
- Find the p-value and confirm your conclusion using the p-value approach.

- A major poll about the Covid-19 vaccination reveals that the proportion of U.S. residents who were hesitant about getting vaccinated was 22% in March. You, the health economist, are interested in conducting your own poll in June to test the hypothesis that this proportion might have changed in June. Out of 100 respondents in your sample, 16 people showed hesitancy.

- Formulate a hypothesis test to determine if the proportion of vaccine hesitancy has changed in June. Write the null and the alternative hypotheses.

- What is the z-score and what is your conclusion at α=0.05? Use the z-score approach to make a conclusion. Do you have sufficient evidence to conclude that this proportion has changed?

- Find the p-value for this sample and confirm your answer using the p-value approach.

- The Department of Transportation states that the average age of cars on the road is more than 12 years. But there is a downward trend in the used car market, and as a researcher, you would like to test the hypothesis that the average age of cars on the road is now less than 12 years. A random sample of 45 cars had an average age of 10.5 years. It is believed that the population standard deviation for the age of cars is 4.1 years.

- Construct a test to see if there has been a decrease in the true average age of the cars on the road. Write the null and the alternative hypotheses.

- What is the z-score and what is your conclusion at α=0.10? Use the z-score approach to make a conclusion. Is your sample evidence sufficient to conclude that the average age is less than 12 years old?
- Find the p-value for this sample and confirm your answer using the p-value approach.