Question

4. Multiple Choice Question Previous experience has shown that the breaking strength of the fabric used in a certain brand of drapes is normally distributed with with a mean of 97 pounds per square inch. A random sample of 9 specimens is examined to reveal an average breaking strength of 7 = 98 pounds per square inch and a standard deviation of 2 pounds per square inch are observed. The p-value to test the hypothesis that the true mean is not 97 is between A. (0.05,0.1) B. (0.1,0.2) C. (0.025,0.05) D. (0,0.025) E. none of the preceding

Answer 1

Claim : True mean is not equal to 97

он
: µ = 97 vs
HO
: µ ≠ 97

Given : = 98 , S = 2 , n = 9

T

Population standard deviation σ is not known therefore we use t statistic.

Test statistic:

t =
X- s/n
= $\frac{98-97 }{2 /\sqrt{9}}$

t = 1.50

As H_a contain ≠ sign , this is two tail test.

df = 9- 1 = 8

two-tail area 0.500 0.250 0.200 0.150 0.100 0.050 0.020 0.010 0.0010 d.f. 0.500 0.750 0.800 0.850 0.900 0.950 0.980 0.990 0.999 с 2 3 4 5 6 7 1.000 2.414 3.078 4.165 6.314 12.706 31.821 63.657 636.619 0.816 1.604 1.886 2.282 2.920 4.303 6.965 9.925 31.599 0.765 1.423 1.638 1.924 2.353 3.182 4.541 5.841 12.924 0.741 1.344 1.533 1.778 2.132 2.776 3.747 4.604 8.610 0.727 1.301 1.476 1.699 2.015 2.571 3.365 4.032 6.869 0.718 1.273 1.440 1.650 1.943 2.447 3.143 3.707 5.959 0.711 1.254 1.415 1.617 1.895 2.365 2.998 3.499 5.408 0.706 1.240 1.397 1.592 1.860 2.306 2.896 3.355 5.041 0.703 1.230 1.383 1.574 1.833 2.262 2.821 3.250 4.781 18

in the row for df = 8 , the test statistic 1.50 lies between values 1.397 and 1.860

Therefore the P value is between 0.1 and 0.2

B. ( 0.1 , 0.2 )