Top Posters
Since Sunday
p
29
29
C
18
I
13
n
13
a
12
11
C
11
s
11
11
m
11
10
New Topic  
wrote...
Posts: 218
2 weeks ago
Vacation days The distribution of the number of vacation days per year offered by different U.S. companies is skewed to the right.

a. We collect data on the number of vacation days from a random sample of 60 companies across the United States. Why is it okay to use these data for inference even though the population is skewed?
b. The mean and standard deviation of the 60 companies in our sample were 22 days and 9 days, respectively. Specify the sampling model (shape, center, spread) for the mean number of vacation days of such samples.
c. Find a 95% confidence interval for the mean number of vacation days offered by U.S. companies.
d. Explain what "95% confidence" means in this context.
Textbook 

Stats: Modeling the World


Edition: 4th
Authors:
Read 47 times
2 Replies
Replies
Answer verified by a subject expert
wrote...
Posts: 257
Rep: 6 0
2 weeks ago
Sign in or Sign up in seconds to unlock everything.
a. We have a large sample size.
b.  t59
c. Conditions:
* Randomization condition: We have a random sample of U.S. companies.
* 10% condition: The sample is less than 10% of the total number of U.S. companies.
* Nearly Normal condition: We know the distribution is skewed, but we have a large enough sample size to proceed.
We can find a t-interval for mean number of vacation days.
We know: n = 60, = 22 , s = 9, and , SE() = = 1.16.
Our confidence interval has the form ± t*n-1 .  We have t*59 = 2.009 (we actually use the critical value for a t with 50 degrees of freedom). Our 95% confidence interval is then
22 ± 2.009 = 22 ± 2.33, or 19.7 to 24.3.
We are 95% confident that the interval 19.7 to 24.3 contains the true mean number of vacation days that are given by U.S. companies.
d. If many random samples of size 60 were taken, 95% of the confidence intervals produced would contain the actual mean number of vacation days offered by U.S. companies.
This verified answer contains over 1490 words.
1

Related Topics

wrote...
2 weeks ago
Thanks
New Topic      
Explore
Post your homework questions and get free online help from our incredible volunteers.
Learn More
Improve Grades
Help Others
Save Time
Accessible 24/7
  141 People Browsing
 102 Signed Up Today
Your Opinion
Do you believe in global warming?
Votes: 186

Previous poll results: Where do you get your textbooks?
Related Images
 553
 454
 3757