Homework SourseThe owner of Weber Chocolates is considering a new machine t
The owner of Weber Chocolates is considering a new machine to create their signature chocolate covered cherry. The present method, hand dipping each cherry takes on average 41.1 seconds to dip and box a dozen cherries. Using the new machine on loan from the salesman to assemble the next 30 boxes they average 39.6 seconds per box. The standard deviation of the sample was 2.4 seconds. Using a 0.05 significance level.
Can you prove that the new machine is faster than the hand dipping method?
What is your null hypothesis?
What is your alternative hypothesis?
What test statistic should you use?
Z-score
t stat
F distribution
p-value
What is the calculated value of the test statistic?
What is the critical value of the test statistic?
What is your decision?
Reject the null hypothesis
Fail to reject the null hypothesis
Reject the alternative
Fail to reject the alternative
Interpret the results:
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| What is your alternative hypothesis?
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![\"x](\"//d2vlcm61l7u1fs.cloudfront.net/bbcswebdav/pid-1061371-dt-content-rid-3391216_1/xid-3391216_1\"/)
![\"x](\"//d2vlcm61l7u1fs.cloudfront.net/bbcswebdav/pid-1061371-dt-content-rid-3391217_1/xid-3391217_1\"/)
![\"x](\"//d2vlcm61l7u1fs.cloudfront.net/bbcswebdav/pid-1061371-dt-content-rid-3391218_1/xid-3391218_1\"/)
![\"x](\"//d2vlcm61l7u1fs.cloudfront.net/bbcswebdav/pid-1061371-dt-content-rid-3391219_1/xid-3391219_1\"/)
![\"x](\"//d2vlcm61l7u1fs.cloudfront.net/bbcswebdav/pid-1061371-dt-content-rid-3391224_1/xid-3391224_1\"/)
![\"x](\"//d2vlcm61l7u1fs.cloudfront.net/bbcswebdav/pid-1061371-dt-content-rid-3391225_1/xid-3391225_1\"/)
![\"x](\"//d2vlcm61l7u1fs.cloudfront.net/bbcswebdav/pid-1061371-dt-content-rid-3391226_1/xid-3391226_1\"/)
![\"x](\"//d2vlcm61l7u1fs.cloudfront.net/bbcswebdav/pid-1061371-dt-content-rid-3391227_1/xid-3391227_1\"/)
![\"x](\"//d2vlcm61l7u1fs.cloudfront.net/bbcswebdav/pid-1061371-dt-content-rid-3391228_1/xid-3391228_1\"/)
![\"x](\"//d2vlcm61l7u1fs.cloudfront.net/bbcswebdav/pid-1061371-dt-content-rid-3391229_1/xid-3391229_1\"/)
![\"x](\"//d2vlcm61l7u1fs.cloudfront.net/bbcswebdav/pid-1061371-dt-content-rid-3391230_1/xid-3391230_1\"/)
Solution
What is your null hypothesis?
x with bar on the top equals mu
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What is your alternative hypothesis?
x with bar on top less than mu
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What test statistic should you use?
t stat
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What is the calculated value of the test statistic?
t=(xbar-mu)/(s/vn)
=(39.6-41.1)/(2.4/sqrt(30))
=-3.42
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What is the critical value of the test statistic?
It is a left-tailed test.
The degree of freedom =n-1=30-1=29
Given a=0.05, the critical value is t(0.05, df=29) =-1.699 (from student t table)
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What is your decision?
Since t=-3.42 is less than -1.699, we reject the null hypothesis.
Reject the null hypothesis
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Interpret the results:
So we can conclude that the new machine is faster than the hand dipping method
