Question

A large company which owns several farms sells potatoes grown on these farms. The company claims that the weights of the potatoes grown on their farms are approximately normally distributed with a mean of 195.6g and a standard deviation of 23.8g. Restaurant A, which buys potatoes from this company, decides to weigh 60 potatoes grown by the company to determine whether the company's claim is true.

(A)Assuming the farm's claim is true, describe the sampling distribution of the sample mean weights for random samples of 60 potatoes.

(B)Restaurant A selects a random sample of 60 potatoes grown by the company and weighs them. They are careful to ensure that the sample is fully random across the entire population of potatoes grown by the company. Restaurant A finds that the mean weight of the potatoes is 190.4g. What is the probability that the mean weight of a random sample of 60 potatoes will be 190.4g or less if the company's claim is true?

(C) Restaurant B also purchases potatoes from the same company and wishes to test the company's claim. However, to simplify the process, they decide to select a sample of 60 potatoes from the closest farm owned by the company. They find that the mean weight of the potatoes in their sample is 180g. Explain why there is a problem with the sampling method used by restaurant B.

Answer 1

(A) sampling distribution of the sample mean weights for random samples of 60 potatoes is defined as

So, sample mean =

Sample standard deviation =

where n=60(sample size) and

this implies,

(B) We have to find the probability that the mean is equal or less than 190.4

.....................equation 1

and

setting the values

{Using z distribution to find the value of 1.692. find 1.6 in left most column and 0.09 in top row}

setting this value in equation 1

we get

P(less than or equal to 190.4) = 1-0.9545 = 0.0455

(C) This is a case of convenience sampling where the Restaurant B owner buys potatoes from the closest farm owned by the company,i.e. it is more convenient for the owner to collect the sample from the closest farm. This will show error in the sampling because it is not a completely probability based sampling, but more of a availability sampling.