Math 136 - Introduction to Statistics » Fall 2021 » Homework 16 HYPOTHESIS TESTING TESTING THE POPULATION STANDARD DEVIATION
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Question #1
A machine dispenses a liquid drug into bottles in such a way that the standard deviation of the contents is 81 milliliters. A new machine is tested on a sample of 24 containers and the standard deviation for this sample group is found to be 26 milliliters. At the 0.05 level of significance, test the claim that the amounts dispensed by the new machine have a smaller standard deviation. Find the test statistic for the question above
A.
χ2= 7.230
B.
χ2=0.237
C.
χ2=3.270
D.
χ2= 2.370
Question #2
A machine dispenses a liquid drug into bottles in such a way that the standard deviation of the contents is 81 milliliters. A new machine is tested on a sample of 24 containers and the standard deviation for this sample group is found to be 26 milliliters. At the 0.05 level of significance, test the claim that the amounts dispensed by the new machine have a smaller standard deviation. Find the critical value for the question above.
A.
13.091
B.
9.131
C.
10.913
D.
1.391
Question #3
A machine dispenses a liquid drug into bottles in such a way that the standard deviation of the contents is 81 milliliters. A new machine is tested on a sample of 24 containers and the standard deviation for this sample group is found to be 26 milliliters. At the 0.05 level of significance, test the claim that the amounts dispensed by the new machine have a smaller standard deviation. Select the conclusion for the question above
A.
Reject Ho
B.
Fail to reject Ho
Question #4
At the α = 0.05 significance level test the claim that a population has a standard deviation of 20.3. A random sample of 18 people yields a standard deviation of 27.1. Find the test statistic for the question above
A.
30.279
B.
33.719
C.
20.179
D.
28.879
Question #5
At the α = 0.05 significance level test the claim that a population has a standard deviation of 20.3. A random sample of 18 people yields a standard deviation of 27.1. Find the critical value for the question above.
A.
8.753, 34.156
B.
6.542, 31.156
C.
4.651, 25.849
D.
7.564, 30.191
Question #6
At the α = 0.05 significance level test the claim that a population has a standard deviation of 20.3. A random sample of 18 people yields a standard deviation of 27.1. Select the conclusion for the question above
A.
Reject Ho
B.
Fail to reject Ho
Question #7
A manufacturer uses a new production method to produce steel rods. A random sample of 17 steel rods resulted in lengths with a standard deviation of 4.5 cm. At the 0.10 significance level, test the claim that the new production method has lengths with a standard deviation different from 3.5 cm, which was the standard deviation for the old method. Find the test statistic for the question above
A.
31.941
B.
26.449
C.
24.439
D.
21.149
Question #8
A manufacturer uses a new production method to produce steel rods. A random sample of 17 steel rods resulted in lengths with a standard deviation of 4.5 cm. At the 0.10 significance level, test the claim that the new production method has lengths with a standard deviation different from 3.5 cm, which was the standard deviation for the old method. Find the critical value for the question above.
A.
9.762, 22.669
B.
6.729, 29.296
C.
2.679, 20.962
D.
7.962, 26.296
Question #9
A manufacturer uses a new production method to produce steel rods. A random sample of 17 steel rods resulted in lengths with a standard deviation of 4.5 cm. At the 0.10 significance level, test the claim that the new production method has lengths with a standard deviation different from 3.5 cm, which was the standard deviation for the old method. Select the conclusion for the question above
A.
Reject Ho
B.
Fail to reject Ho
Question #10
With individual lines at the checkouts, a store manager finds that the standard deviation for the waiting times on Monday mornings is 5.7 minutes. After switching to a single waiting line, he finds that for a random sample of 29 customers, the waiting times have a standard deviation of 4.9 minutes. Use a 0.025 significance level to test the claim that with a single line, waiting times vary less than with individual lines. Find the test statistic for the question above
A.
18.114
B.
26.294
C.
22.546
D.
20.692
Question #11
With individual lines at the checkouts, a store manager finds that the standard deviation for the waiting times on Monday mornings is 5.7 minutes. After switching to a single waiting line, he finds that for a random sample of 29 customers, the waiting times have a standard deviation of 4.9 minutes. Use a 0.025 significance level to test the claim that with a single line, waiting times vary less than with individual lines. Find the critical value for the question above.
A.
18.913
B.
15.308
C.
9.655
D.
11.818
Question #12
With individual lines at the checkouts, a store manager finds that the standard deviation for the waiting times on Monday mornings is 5.7 minutes. After switching to a single waiting line, he finds that for a random sample of 29 customers, the waiting times have a standard deviation of 4.9 minutes. Use a 0.025 significance level to test the claim that with a single line, waiting times vary less than with individual lines. Select the conclusion for the question above
A.
Fail to reject Ho
B.
Reject Ho
Question #13
In one town, monthly incomes for men with college degrees are found to have a standard deviation of $650. Use a 0.01 significance level to test the claim that for men without college degrees in that town, incomes have a higher standard deviation. A random sample of 22 men without college degrees resulted in incomes with a standard deviation of $926. Find the test statistic for the question above
A.
38.66
B.
46.24
C.
42.62
D.
40.12
Question #14
In one town, monthly incomes for men with college degrees are found to have a standard deviation of $650. Use a 0.01 significance level to test the claim that for men without college degrees in that town, incomes have a higher standard deviation. A random sample of 22 men without college degrees resulted in incomes with a standard deviation of $926. Find the critical value for the question above.
A.
38.932
B.
33.322
C.
40.194
D.
35.392
Question #15
In one town, monthly incomes for men with college degrees are found to have a standard deviation of $650. Use a 0.01 significance level to test the claim that for men without college degrees in that town, incomes have a higher standard deviation. A random sample of 22 men without college degrees resulted in incomes with a standard deviation of $926. Select the conclusion for the question above
A.
Reject Ho
B.
Fail to reject Ho
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