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Sagot :
Answer:
There is not sufficient evidence at the 0.01 level that the bags are underfilled or overfilled
Step-by-step explanation:
A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 403 gram setting.
This means that the null hypothesis is:
[tex]H_{0}: \mu = 403[/tex]
Is there sufficient evidence at the 0.01 level that the bags are underfilled or overfilled:
This means that at the alternate hypothesis, we are testing if the mean is different than 403, that is:
[tex]H_{a}: \mu \neq 403[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
Value of 403 tested at the null hypothesis:
This means that [tex]\mu = 403[/tex]
A 10 bag sample had a mean of 411 grams with a variance of 121.
This means that [tex]n = 10, X = 411, \sigma = \sqrt{121} = 11[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{411 - 403}{\frac{11}{\sqrt{10}}}[/tex]
[tex]z = 2.3[/tex]
Pvalue:
Testing if the mean is different of a value, and z positive, which means that the pvalue is 2 multiplied by 1 subtracted by the pvalue of z = 2.3
Looking at the z-table, z = 2.3 has a pvalue of 0.9893
1 - 0.9893 = 0.0107
2*0.0107 = 0.0214
0.0214 > 0.01, which means that there is not sufficient evidence at the 0.01 level that the bags are underfilled or overfilled
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