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An apple farm claims that the average weight of all their apples is 8oz. A sample of 20 apples were picked that had a mean of 7.77oz and standard deviation of 0.95oz. We want to test whether the mean apple weight is different from 8oz. Assume that the apple weights are normally distributed.

User Guang
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1 Answer

6 votes

Answer:

The mean apple weight is different from 8oz

Explanation:

Claim : An apple farm claims that the average weight of all their apples is 8oz.


H_0:\mu \\eq 8\\H_a:\mu = 8

n = 20

Standard deviation =s = 0.95

Since n < 30

So we will use t-test

x = 7.77


t =(x-\mu)/((s)/(√(n)))

Substitute the values :


t =(7.77-8)/((0.95)/(√(20)))


t =−1.0827

Since we are not given the significance level

So, we will take 5%

So,α = 0.05

Degree of freedom = df = n-1 = 20-1 = 19

So, using t table


t_{(\alpha)/(2) , df}=2.093

Since t critical > t statistic

So, we accept the null hypothesis.

So, The mean apple weight is different from 8oz

User Nemenos
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