## Question 861:

1

Question 1
1. We get an observed difference of .106 seconds. The margin of error around this difference is found by using the standard error of the difference between means (SE). The SE is found by averaging the two variances together and dividing each by their sample size to get .2129. The margin is .2129 time the critical value for a 95% confidence interval from the t-distribution on 9 degrees of freedom = 2.26, getting us the margin of +/- .48. That gets us the 95% CI around the difference as between -.5883 and .3750.
2. Since the interval crosses 0 we cannot conclude there is a statistical difference.
3.  It would tell us the lower boundary of the difference between groups. So if we saw a statistical difference and that difference was at LEAST .05, we could conclude the difference was statistically and practically significant.
4. Since there is not enough evidence based on our data to conclude there is an advantage to the new light we would stick with the old one.
Question 2
1. When drivers act as their own control it means the data is setup in a matched design so we can analyze the difference between the times for both conditions. This removes the variability between subjects. It is a good idea since there is so much individual variability between drivers and it will allow us to detect smaller differences in times based on the lights.

2. We have a difference of .1067. The standard error of the difference is equal to the standard deviation of the difference scores divided by the square root of the sample size = .042/SQRT(6) = .0174. The critical value from the t-distribution is 2.57 on 5 degrees of freedom making the margin of error .0174*2.57 = .0448. The 95% confidence interval is between .0618 and .1515 seconds.

3. Yes, since the confidence interval does not cross 0.

4. Since the lower boundary of the confidence interval is at .0618, meaning it is above .05, we can say we're over 95% confident the actual difference is above .0618 and therefore .0618 meaning we have practical and statistical significance.

5. Since there was so much variability between drivers and it is easy to have the same drivers under both conditions it was a good time to used the paired t to increase power.

6. When there would be a learning effect, in which the effects of the first condition affect the results of the second condition.

HW Q1.

We use the z-critical value of 1.96 times the standard error which is SQRT(pq/n) = .0155, getting us a margin of error of .0304 or 3.04%.

HW Q2

We add 3.04% to the proportion .592 getting us an upper boundary of 62.

HW Q3

We subtract the margin of error 3.04 from .592 and get 56.

HW Q4

d)         We reject the null hypothesis and conclude Mr Obama's support is greater than 50%.