We reject the null hypothesis, that is, that the mean weight of the cans is not of 12 ounces of fruit.
Pineapple Corporation (PC) maintains that their cans have always contained an average of 12 ounces of fruit.
This means that the null hypothesis is:
H₀ = µ = 12
The production group believes that the mean weight has changed.
This means that the alternate hypothesis is:
Ha : µ ≠ 12
The test statistic is:
z = X-µ/σ/√n
In which X is the sample mean, µ is the value tested at the null hypothesis, σ is the standard deviation and n is the size of the sample.
12 is tested at the null hypothesis:
This means that µ = 12
They take a sample of 13 cans and find a sample mean of 12.04 ounces and a sample standard deviation of .05 ounces.
This means, that n = 13, X = 12.04, σ = 0.05
Value of the test statistic:
z = X-µ/σ/√n
z = 12.04-12/0.05/√13
= 2.88
P value of the test:
We are testing if the mean is different from a value, which means that the pvalue is 2 multiplied by 1 subtracted by the pvalue of z = 2.88.
Looking at the z-table, z = 2.42 has a pvalue of 0.9980
1 - 0.9980 = 0.002
2*0.002 = 0.004
0.004 < 0.01. This means that at the 0.01 level, we reject the null hypothesis, that is, that the mean weight of the cans is not of 12 ounces of fruit.
Hence we get the require answer.
Learn more about Null hypothesis here:
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