Question

A sample of $20$heads of lettuce was selected. Assume that the population distribution of head weight is normal. The weight of each head of lettuce was then recorded. The mean weight was $2.2$pounds with a standard deviation of $0.1$pounds. The population standard deviation is known to be $0.2$pounds.

What would happen if $40$ heads of lettuce were sampled instead of $20$, and the confidence level remained the same?

Short answer

If the sample size is increased the error will decrease.

Step-by-step solution

Given Information

A sample of $20$heads of lettuce was selected. The mean weight was $2.2$pounds with a standard deviation of $0.1$ pounds. The population standard deviation is known to be $0.2$ pounds.

Explanation

Population standard deviation looks at the square root of the variance of the set of numbers. It's used to determine a confidence interval for concluding (such as accepting or rejecting a hypothesis).