Question

A)

As part of a larger project to study the behavior of stressed-skin panels, a structural component being used extensively in North America, an article reported on various mechanical properties of Scotch pine lumber specimens. Data on the modulus of elasticity (MPa) obtained 1 minute after loading in a certain configuration and 4 weeks after loading for the same lumber specimens is presented here.

Observation	1 min	4 weeks	Difference
1	10,490	9,160	1330
2	16,620	13,250	3370
3	17,100	14,720	2380
4	15,480	12,750	2730
5	12,960	10,120	2840
6	17,260	14,570	2690
7	13,400	11,220	2180
8	13,900	11,100	2800
9	13,630	11,420	2210
10	13,240	10,930	2310
11	14,370	12,110	2260
12	11,700	8,620	3080
13	15,470	12,590	2880
14	17,840	15,090	2750
15	14,070	10,550	3520
16	14,760	12,230	2530

Calculate an upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus; first check the plausibility of any necessary assumptions. (Use α = 0.05. Round your answer to two decimal places.)
MPa=_______

B)

It is thought that the front cover and the nature of the first question on mail surveys influence the response rate. An article tested this theory by experimenting with different cover designs. One cover was plain; the other used a picture of a skydiver. The researchers speculated that the return rate would be lower for the plain cover.

Cover	Number Sent	Number Returned
Plain	207	102
Skydiver	214	109

Does this data support the researchers' hypothesis? Test the relevant hypotheses using α = 0.10 by first calculating a P-value.

Compute the test statistic value and find the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z =
P-value =

C)

Do teachers find their work rewarding and satisfying? An article reports the results of a survey of 396 elementary school teachers and 261 high school teachers. Of the elementary school teachers, 224 said they were very satisfied with their jobs, whereas 125 of the high school teachers were very satisfied with their work. Estimate the difference between the proportion of all elementary school teachers who are satisfied and all high school teachers who are satisfied by calculating a 95% CI. (Use p_elementary − p_{high school}. Round your answers to four decimal places.)

( , )

Answer 1

Ans A ) using minitab>stat>basic stat>Paired t

we have

Paired T-Test and CI: 1 min, 4 weeks

Paired T for 1 min - 4 weeks

N Mean StDev SE Mean
1 min 16 14518 2040 510
4 weeks 16 11902 1897 474
Difference 16 2616 522 130

95% upper bound for mean difference: 2844.91
T-Test of mean difference = 0 (vs < 0): T-Value = 20.06 P-Value = 1.000

an upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus is 2844.91

Ans B ) using excel>addin>phstat>two sample test

we have

Z Test for Differences in Two Proportions
Data
Hypothesized Difference	0
Level of Significance	0.1
Group 1
Number of Items of Interest	102
Sample Size	207
Group 2
Number of Items of Interest	109
Sample Size	214
Intermediate Calculations
Group 1 Proportion	0.492753623
Group 2 Proportion	0.509345794
Difference in Two Proportions	-0.01659217
Average Proportion	0.5012
Z Test Statistic	-0.3404
Lower-Tail Test
Lower Critical Value	-1.2816
p-Value	0.3668
Do not reject the null hypothesis

z =-0.34
P-value =0.3668

C) using excel>addin>phstat >2 sample test

\we have

Z Test for Differences in Two Proportions
Data		Confidence Interval Estimate
Hypothesized Difference	0		of the Difference Between Two Proportions
Level of Significance	0.05
Group 1			Data
Number of Items of Interest	224		Confidence Level	95%
Sample Size	396
Group 2			Intermediate Calculations
Number of Items of Interest	125		Z Value	-1.9600
Sample Size	261		Std. Error of the Diff. between two Proportions	0.0397
			Interval Half Width	0.0778
Intermediate Calculations
Group 1 Proportion	0.565656566		Confidence Interval
Group 2 Proportion	0.478927203		Interval Lower Limit	0.0089
Difference in Two Proportions	0.086729363		Interval Upper Limit	0.1646
Average Proportion	0.5312
Z Test Statistic	2.1799
Two-Tail Test
Lower Critical Value	-1.9600
Upper Critical Value	1.9600
p-Value	0.0293

95% confidence interval is ( 0.0089 ,0.1646)