Question

1. In an effort to reduce energy costs, a major university has installed more efficient lights as well as automatic sensors that turn the lights off when no movement is present in a room. Historically, the cost of lighting an average classroom for 1 week has been $265. To determine whether the changes have signficantly reduced costs, the university takes a sample of 50 classrooms. They find that the average cost for 1 week is $247 with a standard deviation of $60. When testing the hypothesis (at the 5% level of significance) that the average energy use has decreased from the past, what is the p-value? (please round your answer to 4 decimal places)

2. An online stock trading company makes part of their revenue from clients when the clients trade stocks therefore, it is important to the company to have an good idea of how many trades its clients are making in a given year. In a sample of 84 clients of an online stock trading company, the average number of trades per year was 58 with a standard deviation of 20. Find the LOWER bound of the 95% confidence level of the average number of trades the company’s clients make. (please express your answer using 2 decimal places)

3. Suppose that a grocery store buys milk for $2.10 and sells it for $2.60. If the milk gets old then the grocery store can sell their unsold milk back to their wholesaler for $0.60 (so the grocery store loses $1.50 on each gallon that it has to sell back to the wholesaler). Suppose that the demand for milk is normally distributed with a mean of 2,226 gallons per week and a standard deviation of 408 gallons per week. The grocery store needs to decide how much milk to order. Suppose that instead of trying to maximize their expected profits, the store wanted to be 90% sure that they have enough milk to satisfy demand. How much milk should they order?

4. Suppose that the number of guests per month that members of a country club bring to golf is given by the following probability distribution:
56% of the members don't have any guests each month, 17% of the members have 1 guest per month to the club; 10% of the members have 2 guests per month; and the remaining members have 3 guests per month.
What is the expected value of the number of guests that members bring out each month? (please express your answer using 2 decimal places)

5. An online stock trading company makes part of their revenue from clients when the clients trade stocks therefore, it is important to the company to have an good idea of how many trades its clients are making in a given year. In a sample of 103 clients of an online stock trading company, the average number of trades per year was 80 with a standard deviation of 16. If you were to test the hypothesis that theaverage number of trades per year is different than the previous year when the average number of trades was 85 (using the % level of significance), what is the test statistic? (please round your answer to 2 decimal places)

Answer 1

We would be looking at question 1 here as:

Q1) As we are testing here whether the cost of lighting an average classroom for 1 week is less than $265, therefore the test statistic here is computed as:

For n - 1 = 49 degrees of freedom, we get the p-value from the t distribution tables here as:
p = P( t49 < -2.1213) = 0.0195

Therefore 0.0195 is the required p-value here.

As the p-value here is 0.0195 < 0.05 which is the level of significance, therefore we have sufficient evidence here that the average cost for 1 week is less than $265