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.

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.

n = 20

Standard deviation =s = 0.95

Since n < 30

So we will use t-test

x = 7.77

Substitute the values :

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

Since t critical > t statistic

So, we accept the null hypothesis.

So, The mean apple weight is different from 8oz

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).