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

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.

$H_0:\mu \neq 8\\H_a:\mu = 8$

n = 20

Standard deviation =s = 0.95

Since n < 30

So we will use t-test

x = 7.77

$t =\frac{x-\mu}{\frac{s}{\sqrt{n}}}$

Substitute the values :

$t =\frac{7.77-8}{\frac{0.95}{\sqrt{20}}}$

$t =−1.0827$

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

$t_{\frac{\alpha}{2} , df}=2.093$

Since t critical > t statistic

So, we accept the null hypothesis.

So, The mean apple weight is different from 8oz