Part 1. (8.49) Computer programmer A always drove to work, whereas programmer B took the bus.
Programmer A claimed that is was quicker, on average, to go by car. The programmers recorded the
following travel times in minutes for each of 10 days:
 

Day	A Time by car	B Time by bus
1	18.9	19.9
2	15.9	18.3
3	17.9	16.9
4	19.2	18.9
5	15.7	20.2
6	16.9	19.5
7	16.4	16.7
8	16.8	19.1
9	19.0	17.9
10	17.1	20.3

List the difference x = A - B and verify that its mean is -1.390 and s = 1.896. With a 5% significance level, is there enough evidence
to support programmer A's claim? Assume the population of differences is approximately normal.

(a) Use the classical approach.    (b) Use the P-value approach.

Part 2. Parts (a) and (b) assume the information was obtained with independent random samples from populations A and B.

(a) Test the claim that the means of  populations A and B are the same. Use a 5% level of significance.
The sample information is given in the table.
 

Population	n	mean	variance
A	40	315	400
B	60	324	360

(b) Test the claim that the means of  populations A and B are the same. Use a 5% level of significance.
The sample information is given in the table.
 

Population	n	mean	standard deviation
A	18	4.8	4.3
B	16	6.9	12.7

Part 3. A manufacturer wanted to compare the quality of work produced by two shifts. from each shift 300 items were selected.
Six percent of the items manufactured by shift A were found to be defective, and 4% of the items manufactured by shift B were defective.
Is there sufficient evidence to indicate a difference in the population proportion of defectives produced by the two shifts?
Use a 5% level of significance.
 

profesor@pindling.org