18) A city council must decide whether to fund a new "welfare-to-work" program to assist long-time unemployed people in finding jobs. This program would help clients fill out job applications and give them advice about dealing with job interviews. A six-month trial has just ended. At the start of this trial a number of unemployed residents were randomly divided into two groups; one group went through the help program and the other group did not. Data about employment at the end of this trial are shown in the table (below). Should the city council fund the program? Test an appropriate hypothesis and state your conclusion.
I'm unsure whether to use a two-proportional z-test or two-proportional z-interval. My hypotheses are "Ho: p1=p2" and "Ha: p1≠ p2". Is that correct, or should that be vice-versa?
I used a two-proportional z-test and get a p-value of 0.3401, which suggests no difference in unemployment and is strong evidence for the null.
19) At one vehicle inspection station, 13 of 52 trucks and 11 of 88 cars failed the emissions test. Assuming these vehicles were representative of the cars and trucks in that area, what is the standard error of the difference in the percentage of all cars and trucks that are not in compliance with air quality regulations?
I used a two proportional z-interval to get SE = 0.0696. Yay or nay?
20) Suppose that a manufacturer is testing one of its machines to make sure that the machine is producing more 97% good parts (H<sub>0</sub>: p = 0.97, H<sub>A</sub>: p > 0.97). The test results in a P-value of 0.122. Unknown to the manufacturer, the machine is actually producing 99% good parts. What probably happens as a result of the testing?
scan of exercises
Code:
+--------------+-------+---------+
| | Current status |
| | Empl. | Unempl. |
+ -------------+-------+---------+
| Group 1 | 20 | 34 |
| (Help prog.) | | |
+--------------+-------+---------+
| Group 2 | 13 | 33 |
| (no help) | | |
+--------------+-------+---------+I used a two-proportional z-test and get a p-value of 0.3401, which suggests no difference in unemployment and is strong evidence for the null.
19) At one vehicle inspection station, 13 of 52 trucks and 11 of 88 cars failed the emissions test. Assuming these vehicles were representative of the cars and trucks in that area, what is the standard error of the difference in the percentage of all cars and trucks that are not in compliance with air quality regulations?
I used a two proportional z-interval to get SE = 0.0696. Yay or nay?
20) Suppose that a manufacturer is testing one of its machines to make sure that the machine is producing more 97% good parts (H<sub>0</sub>: p = 0.97, H<sub>A</sub>: p > 0.97). The test results in a P-value of 0.122. Unknown to the manufacturer, the machine is actually producing 99% good parts. What probably happens as a result of the testing?
scan of exercises