The average weight of a package of rolled oats is supposed to be at least 18 ounces. A sample of 18 packages shows a mean of 17.78 ounces with a standard deviation of 0.41 ounces. At the 5% level of significance, is the true mean smaller than the specification?

Question

Elise Tran

Mathematics

8 December, 04:03

The average weight of a package of rolled oats is supposed to be at least 18 ounces. A sample of 18 packages shows a mean of 17.78 ounces with a standard deviation of 0.41 ounces. At the 5% level of significance, is the true mean smaller than the specification?

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Mango · Answer 1

Step-by-step explanation:

The average weight of a package of rolled oats is supposed to be at least 18 ounces

Null hypothesis: u > = 18

Alternative: u < 18

Using the t-test formula, we have

t = x-u / (sd/√n)

Where x is 17.78, u = 18, sd = 0.41 and n = 18

t = 17.78-18 / (0.41/√18)

t = - 0.22 / (0.41/4.2426)

t = - 0.22 / 0.0966

t = - 2.277

Since, this is a left tailed test, at a significance level of 0.05, the p value is 0.01139. Since the p value is less than 0.05, we will reject the null hypothesis and conclusion that the true mean smaller than the actual specification.