Homework Assignment #6

Total: 20 points

Instructions:

1. Read the instructions for each question carefully. When required, show all your solutions for each question. You will not merit full points for failure to follow the instructions.

2. You may submit your homework in either excel or word file. If it is a word file, cut and paste your PhStat solutions. Do not convert it to PDF file.

3. Properly label your final answers in excel or word file.

Question 1. (1 point)

If you use a 0.01 level of significance in a two-tail hypothesis test, state your DECISION RULE for rejecting Ho: µ = 12.5 if you use a Z test?

Note: Decision rule is different from decision.

Question 2. Note that this problem requires PhStat solution. (6 points)

The quality-control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7,500 hours. The population standard deviation is 1,000 hours. A random sample of 64 CFLs indicate a sample mean life of 7,250 hours.

1. At 0.05 level of significance, state your decision.

2. Using the critical value approach, is there evidence that the mean life is different from 7,500 hours?

3. Determine the p-value and interpret its meaning.

4. Construct and interpret a 95% confidence interval estimate of the population mean life of the CFLs.

Question 3. Note that this problem requires PhStat solution. (4 points)

A marketing researcher wants to estimate the mean amount spent ($) on Amazon.com by Amazon Prime member shoppers. Suppose a random sample of 100 Amazon Prime member shoppers who recently made a purchase on Amazon.com yielded a mean amount spent of $1,500 and a standard deviation of $200.

1. Using a 0.05 level of significance, state your decision.

2. Using the critical value approach, is there evidence that the population mean amount spent on Amazon.com by Amazon Prime member shoppers is less than $1,475?

3. Determine the p-value and interpret its meaning.

Question 4. Note that this problem requires PhStat solution. (5 points)

The population mean waiting time to check out of a supermarket has been 4 minutes. Recently, in an effort to reduce the waiting time, the supermarket has experimented with a system in which infrared cameras use body heat and in-store software to determine how many lines should be opened. A sample of 100 customers was selected, and their mean waiting time to check out was 4.25 minutes with a sample standard deviation of 2.7 minutes.

1. State your decision rule.

2. What is your decision?

3. At 0.05 level of significance, using the critical value approach, is there evidence that the population mean waiting time to check out is greater than 4 minutes?

4. Determine p-value and interpret its meaning.

Question 5. Note that this problem requires PhStat solution. (4 points)

A cellphone provider has the business objective of wanting to determine the proportion of subscribers who would upgrade to a new cellphone with improved features if it were made available at a substantially reduced price. Data are collected from a random sample of 550 subscribers, and the result indicate that 150 of the subscribers would upgrade to a new cellphone at reduced cost.

1. State the null and alternative hypotheses. Observe the proper format.

2. At 0.05 level of significance, state your decision.

3. Is there evidence that more that 20% of the customers would upgrade to a new cellphone at a reduced cost?