Show as much work as possible. For the hypothesis testing problems, be sure to state the null and alternative hypothesis, find the test statistic and critical value(s), and state your conclusion concerning the null hypothesis.

 

1)  A computer firm offers a retirement program for their employees. Of the employees over the age of 35, 75% participate in the retirement. Furthermore, 55% of the employees participate in the retirement program. Finally, 40% of the employees are under the age of 35.

a)  What is the probability that a randomly chosen employee is over 35? (5)  

b)  What is the probability that a randomly chosen employee is over 35 or participates in the retirement program? (5)

c)  What is the probability that a randomly chosen employee is under 35 and participates in the retirement program? (5)

d)  Of the employees who participate in the retirement program, what is the probability that they are under 35? (5)  

e)  Of the employees who are over 35, what is the probability that they participate in the retirement program? (5)

 

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 120 clients of an online stock trading company, the average number of trades per year was 82 with a standard deviation of 16. 

a)  Find the 99% confidence level of the average number of trades the company’s clients make. (10)

b)  Test the hypothesis at the 10% level of significance, that the average number of trades per year is different than the previous year when the average number of trades was 85. (15)

d)  Suppose that we wanted to estimate the average number of trades an online stock trading company’s clients made and we wanted to be 98% sure that the estimate was within 2 trades of the true average. How large a sample would need to be taken (using the standard deviation of 16  mentioned above)? (8) 

e)  Suppose that we wanted to estimate the proportion of an online stock trading company’s clients that made at least 100 trades in a year and we wanted to be 95% sure that the estimate was within 2% trades of the true proportion. How large a sample would need to be taken? (8) 

  

3)  In the past, the number of guests golfing at a local country club has averaged 120 per week. Over the past 16 weeks, the average number of guests has been 135 with a standard deviation of 15. If the club is pretty sure that the average number of guests is now higher than in the past (when it was 120) then it will lower the dues of the members (but they only want to do this if they are pretty sure that the average number of guests is now higher than it was before). At the 10% level of significance, test the hypothesis that the average number of guests is now greater than the 120 observed in the past? (15) 

 

 

4)  A local firm is trying to decide what it would cost the company if they changed their retirement program. First, they must examine the proportion of employees that they expect to participate in the program. In a preliminary survey of 120 employees 73% said that they would participate in the new program.

a)  Determine a 95% confidence interval for the proportion of employees who would participate in the new program. (10)

b)  Test the hypothesis at the 10% level of significance that at least 80% of the employees will participate in the new program. (15)

c)  What is the p-value? (5)

 

5)  For revenue projections, the manager of a country club needs to know how many guests the members of the club bring to the club to golf. Suppose that the number of guests that golf in a given week is normally distributed with a mean of 120 and a standard deviation of 18. 

a)  What is the probability that on a single randomly chosen week that at least 140 guests golf? (10)

b)  What is the probability that in a sample of 36 weeks that the number of guests average at least 115? (15)

 

 

6)  Suppose the profit the Honda dealership makes on the next 4 Accords it sells are 800  1100  750  1550  

a)  What is the average profit the dealership made on these cars? (5)

b)  What is the standard deviation of the profits the dealership made on these cars? (8)

 

7)  Suppose that the number of guests per month that members of a country club bring to golf is given by the following probability distribution:

a)  What is the expected number of guests that members bring to golf in a given month? (8)

b)  What is the standard deviation of the number of guests per member? (10)

c)  What is the probability that in a sample of 120 members that at least 25% of them brought at least 2 guests to golf last month? (10)

 

8)  Suppose that a company knows that on average, 30% of guests at a hotel will eat at the hotel restaurant.

a)  What is the probability that in a sample of 8 guests that at least 2 eat at the hotel restaurant? (8)

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