Statistic exercise
Xyq012074
Stat2103-exercise.docxName:_________
(1) (10 pts) Below the manager level, salaries of at a consulting firm are distributed as a normal random variable with a mean of $50,000 and a standard deviation of $8,000. The distribution of salaries is roughly symmetric and uni-model. If a random sample of 64 employees is selected, what is the probability the sample mean will exceed $52,000?
(2) (15 pts) The referee at a football game against a rival school tosses a coin to see which team receives the opening kick-off. You suspect the coin is not fair. After 400 coin tosses, you get 175 heads and 225 tails.
a. Construct a 95% confidence interval for the long-term population proportion of heads.
b. If you wanted to test the hypothesis that this coin is not fair, what would be the null and alternative hypotheses?
H0:
HA:
c. If you wanted to test the hypothesis that this coin is not fair, what would be your conclusion (use your result from part a.)?
(3) (20 pts) The following sample of wages for waiters (including tips) during randomly selected one-hour periods at a popular chain restaurant was taken: $19, $23, $24, $14, and $20. Use this data to determine if the long term average hourly wage for waiters at this chain is above $18.
a. What are the null and alternative hypotheses?
b. What is the observed value of the appropriate test statistic?
c. What is the P-value of the test statistic?
d. Does the data show that long term average hourly wage for waiters at this chain is above $18? State your conclusion at the α=5% level of significance.
(4) (15 pts) A local restaurant tried to increase revenue with a promotion campaign posting 10%-off coupons on their website. The observed revenue for the week (they close on Monday) before and after the promotion are shown below. Do the data show that the promotional campaign increased revenue?
|
|
Revenue ($1,000) |
|
|
|
Before Promo |
After Promo |
|
Tue |
7.4 |
10 |
|
Wed |
8.1 |
10.6 |
|
Thurs |
8.6 |
7.7 |
|
Fri |
11.2 |
12.8 |
|
Sat |
13.7 |
15.8 |
|
Sun |
12.1 |
11.8 |
a) What are the null and alternative hypotheses?
b) What is the observed value of the appropriate test statistic?
c) What is the P-value of the test statistic?
d) Does the data show that the promotional campaign increased revenue? State your conclusion at the α=10% level of significance.
