Question

Can someone help me by answering #2 of these questions.

Using the techniques described in sections 10.2 and 10.3 of the text, for each of these hypothesis testing problems, (a) state the null and alternative hypotheses, (b) determine the critical value(s), (c) calculate the test statistic, (d) decide whether or not to reject the null hypothesis, and (e) write a full conclusion in the context of the problem 1. A group of people were asked the question, "If you received an envelope addressed to your neighbor that contained a $100 bill, would you keep it instead of passing it on? Of the 185 men in the group 21 said Yes, and of the 163 women in the group, 25 said Yes. Do these data indicate that the proportions are different for men and women at the 5% level of significance? 2. In a manufacturing plant a new machine was purchased to perform precision parts calibration. The times (in seconds) needed by the new machine and the old machine to calibrate randomly chosen part lots is given in the table to the right. Is the new machine faster than the old machine? Use α= 0.05 [No need to use Satterthwaite's approximation.] Old 13.314.0 14.910.1 8.7 6.4 17.9 10.7 12.8 15.0 15.0 7.918.3 11.515.4 New 13.9 11.1 7.3 8.9 12.9

Answer 1

2)

New	Old	Difference(d)
13.3	14	-0.7
14.9	10.1	4.8
13.9	8.7	5.2
6.4	17.9	-11.5
11.1	10.7	0.4
7.3	12.8	-5.5
8.9	15	-6.1
12.9	15	-2.1
7.9	18.3	-10.4
11.5	15.4	-3.9
	Total	-29.8

a)

Claim: The new machine faster than the old machine.

The null and alternative hypothesis is

$H0:\mu_{d}=0$

$H1:\mu_{d}>0$

b)

Level of significance = 0.05

Degrees of freedom = n - 1 = 10 - 1 = 9

Critical value = 1.833   ( Using t table)

c)

Sample size = n = 10

Sample mean of difference = $\bar{d}$ = - 2.98

Sample standard deviation of difference = $s_{d}$ = 5.6707

Test statistic is

$t=\frac{\bar{d}}{s_{d}/\sqrt{n}}$

d)

一2.98 5.6707/YW =-1.66

Test statistic | t | < critical value we fail to reject the null hypothesis.

e)

Conclusion:

The new machine NOT faster than the old machine.