Assume that the U.S. Mint manufactures dollar coins so that the standard deviation is 0.0410 g. The accompanying list contains weights (grams) of dollar coins manufactured with a new process designed to decrease the standard deviation so that it is less than 0.0410 g. This sample has these summary statistics: n= 16, x8.065 g, s = 0.03 g. A 0.10 significance level is used to test the claim that the sample is from a population with a standard deviation less than 0.0410 g. The null and alternative hypotheses are Ho: o = 0.0410 g and H,:0<0.0410 g. For this sample data, we get a P-value of 0.0174 when testing the claim that o<0.0410 g. Complete parts (a) through (c). A Click the icon to view the weights of dollar coins manufactured with the new process. a. What should we conclude about the null hypothesis? A. Fail to reject the null hypothesis. O B. Reject the null hypothesis. OC. Accept the null hypothesis. O D. Fail to accept the null hypothesis. b. What should we conclude about the original claim? V sufficient evidence to V the claim that the sample is from a population with a standard deviation less than 0.0410 g. There c. What do these results suggest about the new minting process? V evidence that the V than the old method, since there Based on this result, the new minting process weights of coins produced by this process
Assume that the U.S. Mint manufactures dollar coins so that the standard deviation is 0.0410 g. The accompanying list contains weights (grams) of dollar coins manufactured with a new process designed to decrease the standard deviation so that it is less than 0.0410 g. This sample has these summary statistics: n= 16, x8.065 g, s = 0.03 g. A 0.10 significance level is used to test the claim that the sample is from a population with a standard deviation less than 0.0410 g. The null and alternative hypotheses are Ho: o = 0.0410 g and H,:0<0.0410 g. For this sample data, we get a P-value of 0.0174 when testing the claim that o<0.0410 g. Complete parts (a) through (c). A Click the icon to view the weights of dollar coins manufactured with the new process. a. What should we conclude about the null hypothesis? A. Fail to reject the null hypothesis. O B. Reject the null hypothesis. OC. Accept the null hypothesis. O D. Fail to accept the null hypothesis. b. What should we conclude about the original claim? V sufficient evidence to V the claim that the sample is from a population with a standard deviation less than 0.0410 g. There c. What do these results suggest about the new minting process? V evidence that the V than the old method, since there Based on this result, the new minting process weights of coins produced by this process
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Transcribed Image Text:Assume that the U.S. Mint manufactures dollar coins so that the standard deviation is 0.0410 g. The accompanying list contains weights (grams) of dollar coins
manufactured with a new process designed to decrease the standard deviation so that it is less than 0.0410 g. This sample has these summary statistics: n= 16,
x = 8.065 g, s= 0.03 g. A 0.10 significance level is used to test the claim that the sample is from a population with a standard deviation less than 0.0410 g. The null
and alternative hypotheses are Ho: o = 0.0410 g and H,:0<0.0410 g. For this sample data, we get a P-value of 0.0174 when testing the claim that o < 0.0410 g.
Complete parts (a) through (c).
E Click the icon to view the weights of dollar coins manufactured with the new process.
...
a. What should we conclude about the null hypothesis?
O A. Fail to reject the null hypothesis.
O B. Reject the null hypothesis.
C. Accept the null hypothesis.
ols
O D. Fail to accept the null hypothesis.
b. What should we conclude about the original claim?
sufficient evidence to
V the claim that the sample is from a population with a standard deviation less than 0.0410 g.
There
c. What do these results suggest about the new minting process?
V than the old method, since there
evidence that the
Based on this result, the new minting process
weights of coins produced by this process
Expert Solution
Step 1
Given that
Population standard deviation =0.0410
Sample size=16
Sample mean=8.065
Sample standard deviation =0.03
Significance level=0.10
P value =0.0174
We have to draw conclusion about the claim that the samples is from a population with a standard deviation less than 0.0410 g ..
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