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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.

Answer :

Answer:

The mean apple weight is different from 8oz

Step-by-step explanation:

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

[tex]H_0:\mu \neq 8\\H_a:\mu = 8[/tex]

n = 20

Standard deviation =s = 0.95

Since n < 30

So we will use t-test

x = 7.77

[tex]t =\frac{x-\mu}{\frac{s}{\sqrt{n}}}[/tex]

Substitute the values :

[tex]t =\frac{7.77-8}{\frac{0.95}{\sqrt{20}}}[/tex]

[tex]t =−1.0827[/tex]

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

[tex]t_{\frac{\alpha}{2} , df}=2.093[/tex]

Since t critical > t statistic

So, we accept the null hypothesis.

So, The mean apple weight is different from 8oz

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