Question

Use the following information to answer the next three questions.

A high school statistics class wants to estimate the average cookie weight of a generic brand of chocolate chip cookies. They collect a random sample of 50 cookies from the manufacturing process and obtain the weight (in grams) for each cookie. Based on their data, the 95% confidence interval for the average weight per cookie is 25.65 to 26.35 grams.

Indicate whether the following is a valid or invalid conclusion.

We can infer with 95% confidence that a randomly selected cookie manufactured for this generic brand will weigh between 25.65 to 26.35 grams. (Valid or Invalid)

We can infer with 95% confidence that mean weight of all cookies manufactured for this generic brand is between 25.65 and 26.35 grams. (Valid or Invalid)

We can infer with 95% confidence that the average weight for 50 cookies randomly selected from those manufactured for this generic brand will be between 25.65 and 26.35 grams. (Valid or Invalid)

Answer 1

we know that the 95% confidence interval range is 25.65 g to 26.35 g

We know that we calculate the confidence interval for the population mean but not for the sample mean.

option A is invalid because it is saying that the confidence interval is calculated for a randomly selected cookie

option B is valid because it is saying that the mean weight of all cookies, i.e. the population average is between the given range

option C is invalid because it is saying that the confidence interval is calculated for the sample mean

So, option B is valid answer