ISDS 361B
HOME WORK 2
INFERENCES ABOUT MEANS AND PORORTIONS
FOR TWO POPULATIONS
USE EXCEL TO DO ALL QUESTIONS
Remember, McClave is incorrect about large and small samples – that is not the criterion for which test to use. The steps are as follows:
- Is the data paired? – If YES, do a matched pairs test:
Excel test:t-test Paired Two Sample for Means
- If the data is not paired, are the variances known? -- If YES, do 2-population z-test.
Excel test:z-test Two Sample for Means
- If the standard deviations are not known, determine whether or not you can assume that the standard deviations are equal:
Excel test:F-test Two Sample for Variances
Multiply the p-value for the 1-tail test by 2 since this is a 2-tail test.
- If the p-value for the 2-tail F-test is low –
This means you conclude that the variances differ. Then do:
Excel test:t-test Two Sample Assuming Unequal Variances
- If the p-value for the 2-tail F-test is high –
This means you cannot conclude that the variances differ. Then do:
Excel test:t-test Two Sample Assuming Equal Variances
1)MCCLAVE Book, Page 380, Question 7.2
2)MCCLAVE Book, Page 380, Question 7.3
Assuming standard deviations of population 1 and 2 are known as 1 = 150 and 2 = 200. In order to compare the means of two populations, independent random samples of 400 observations are selected from each population with 1 = 5,275 and 2 = 5,240. Do problem (a), (b), (c), (d) as stated
3)The international Air Transportation Association surveyed business travelers to determine ratings of various international airports. The maximum possible rating score was 10. Suppose 50 business travelers were asked to rate the Miami airport, and 50 other business travelers were asked to rate the Los Angeles airport. The rating scores are stored in Airport.
a)Assuming standard deviations of Miami ratings and Los Angeles ratings are known as 12 = 2.2 and 22 = 2.4, develop a 95% confidence interval estimate of the difference between the mean ratings of the Miami and Los Angeles airport.
b)How many travelers in Miami and Los Angeles should be surveyed to estimate the true average difference in rating to within 0.5?
c)Assuming standard deviations of Miami rating and Los Angeles ratings are not known; develop a 95% confidence interval estimate of the difference between the mean ratings of the Miami and Los Angeles airport.
4)MCCLAVE Book, Page 380, Question 7.6a
5)MCCLAVE Book, Page 381, Question 7.12
Table below gives the means and standard deviations of carat sizeof diamonds certified by HRD and GIA
a)Construct a 95% confidence interval for the difference between the mean carat size of diamonds certified by HRD and GIA
b)From the summary data given above, do the data provide sufficient evidence to conclude the HRD - GIA > .11 carats?
6)MCCLAVE Book, Page 381, Question 7.12
a)Using the data set provided in worksheet diamond, do the data provide sufficient evidence to conclude that the difference between average HRD price and GIA price ≠ $2500
b)Construct a 95% confidence interval for the difference between the mean price of diamonds certified by HRD and GIA
7)In order to compare the means of two populations; independent sample of 150 observations are selected from each population with the following results:
Assume that the variances of two populations are equal.
a)At α= 5%, can you conclude that two population means differ?
b)Construct a 95% confidence interval to estimate the difference between population means (1 - 2)
8)A paired difference experiment produces the following results:
N = 25
= -3.5
= 21
a)At α= 5% can you conclude that 1 and 2 differ?
b)What assumptions are necessary so that the paired difference test will be valid?
c)Construct a 95% confidence interval to estimate the mean difference D
9)MCCLAVE BOOK, Page 393, Question 7.30
a)As stated
b)As stated
c)As stated
d)At α= 10%, can you conclude that salary has increased between 2003 and 2005?
e)Construct a 90% confidence interval to mean difference of salary between 2003 and 2005
Homework 2 - Question1