Question

A company has states that their straw machine makes straws that are 4 mm diameters. A worker believes the machine no longer makes straw of the size and sample 100 straws to perform a hypothesis test with 99% confidence.

Answer 1

To find the mean diameter and standard deviation for the sample, calculate the average and standard deviation of the 100 straws' diameters. To determine if the company's diameter claim is plausible, find the probability that 50 randomly selected screws will be within the stated tolerance levels.

Step-by-step explanation:

To find the mean diameter and standard deviation for the sample, we need to calculate the average and standard deviation of the 100 straws' diameters.

a. Mean diameter = sum of all diameters / number of straws = (diameter1 + diameter2 + ... + diameter100) / 100. Standard deviation = the square root of the sum of the squared differences between each diameter and the mean, divided by the number of straws - 1.

b. To find the probability that 50 randomly selected screws will be within the stated tolerance levels, we need to calculate the z-score and use a z-table or a statistical calculator to find the area under the normal distribution curve. If the probability is high (close to 1), then the company's diameter claim is plausible.