Problem 5.6
The mean is 71. The t score for 95% and 24 d.f. is 2.06. 77 is the mean + s.e.*t. This leads to a standard error of 2.913. Sigma is 2.913 * 5 = 14.563.
Problem 5.14
a) Z * s.e. = 25/2. For a two-tailed 90 % test, Z= 1.645, the goal for standard error is 7.599. sqrt(250) = 15.811. 15.811/sqrt(N) = 7.599. She needs 5 samples.
b) For a 99% confidence interval to be the same, Z is larger. s.e. must be smaller. Since sqrt(n) is in the denominator, the sample size must be larger.
c) 12.5 = Z * s.e. Z = 2.576. S.E. = 4.852. sqrt(N) = 3.26. He needs 11 samples.
Problem 5.20 a) There is no obvious difference between the mean reading score and mean writing score.
b) The reading and writing scores are not independent.
c) h0 : reading and writing scores have the same mean. H1 : reading and writing scores are different.
d) The conditions for inference are not met. It is unlikely that scores are independent. It’s reasonable to assume a better reader is also a better writer.
e) (-.545-0)/8.887 = -.061. There is no evidence to reject the null hypothesis. f) Our power of the test is very weak. Sigma is extremely high. We might have a type 2 - error. A type 1 error would not be possible since we didn’t come close to rejecting the null hypothesis.
g) It’s likely our confidence interval will include 0. Our sigma is very high and we observed a mean very close to 0.
Problem 5.32
Our data provides strong evidence that there is a differnce in fuel economy between standard and automatic cars sold in 2012. standard error = sqrt(3.582/26 +4.512/26) 1.1292697 T=2.787 for 25 d.f. and a two-tailed test with a .01 level of confidence. Our t-value is 3.30, calculated as the quotient of the difference between sample means and standard error.
Problem 5.48
a) H0: Average work hours do not vary across the educational attainment groups studied.
H1: There are at least two means among our data that are different.
b)Our conditions for inference seem to be met. We believe the General Social Survey has randomly sampled the population. The size of each group is >30 and is not >10% of the population. The Bachelor’s degree group is skewed but the sample size is large.
c)
| degree |
4 |
2006.16 |
501.54 |
2.188993 |
0.0682 |
| residuals |
1167 |
267382 |
229.119 |
|
|
| total |
1171 |
269388.16 |
|
|
|
The threshold for the F-test at .05 confidence level is 2.3719. Our F-value is 2.188993. We cannot reject the null hypothesis that Average working hours do not vary across educational attainment groups.