Question

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 1

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