1) In a sample of 45 women who worked at company their average yearly salary was $63,000 with a standard deviation of $10,000

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1) In a sample of 45 women who worked at company their average yearly salary was $63,000 with a standard deviation of $10,000. In a sample of 56 men at the company in similar jobs their average yearly salary was $67,000 with a standard deviation of $12,500.

a) At the .01 level is there a difference in the average salary of the men and women at this company? (p = .084)

 

b) Based on the answer for a) would a claim by a woman of sexism in salaries be legitimate? Explain

 

 2. A sample of 100 people were given a tour of a winery and then shown the process of how the wine was produced. The group of 100 was then given samples to taste of the wine and 48 rated the wine as "excellent." For a separate group of 120 people who were simply given the wine without the tour or being shown the process 20 rated the wine as "excellent" a) At the .05 level was there a difference in the % of people who rated the wine excellent? (p = 0)

b) Based on the answer for a) what appears to be the reason for the difference in the % of the two groups?

 

6. Currently a company has 47% of their employees enrolled in a 401(k) program (this is a retirement program with tax deferrals on income). The company wishes to increase the % of employees in this program. To do that they require each employee to attend a seminar that demonstrates the incredible savings impact that the 401(k) offers for the employees. In a sample of 120 employees who attended the seminar 89 joined the 401(k) program.

a) At the .01 level did the seminar increase the % of employees in the program? (p-value = 0)

b) Interpret the p-value obtained in a)

c) Find and interpret the 99% confidence interval (computer says "lower bound is .6474")

 

 

 3. You sell big screen TV's for a price of $780. You wish to see if the consumer's idea of the price of your TVs is different. In a sample of 27 consumers, when asked "how much do you think this big screen TV costs?" the average price was $830 with a standard deviation of $150.

 

a) At the .01 level is the consumer's idea of the average price different from your price? (p = .095)

 

b) Find and interpret the 99% confidence interval (computer gives (749.79, 910.21))

 

c) If I take another sample of 27 consumers and ask them how much they think the big screen TV costs would an average price of $800 be something that you would expect to occur? explain

 

d) What is the only type of error that could have occurred in this problem? (no explanation of error needed)

 

 4. Engagement rings on average cost $6000. In a sample of 56 dating couples they were asked how much they would spend on their engagement rings and the average was $5300 with a standard deviation of $1200.

 

a) At the .05 level is the price of what the couples were willing to spend statistically significantly different than average? (p = 0)

 

b) Find and interpret the 95% confidence interval (computer says (4978.6,5621.4)) (11)

 

5. In a roulette wheel the color red occurs 48.7% of the time. You think the casino is cheating because the number red appears to be coming up less than expected. Why do you say this? In  a sample of the last 230 spins of the roulette wheel red came up 105 times.

 

a) At the .01 level is red coming up at a statistically significant lower amount than expected? (p-value = .178)

 

b) What is the reason for the difference for red coming up at a lower % based on the answer for a)