Question

You work at a factory located at the North Pole. The toy you are making is supposed to measure 10” long. From experience, the lengths of toys produced follow a Normal distribution with standard deviation σ = 0.3 inches. You believe that new elves are producing toys that are less than 10 inches. As supervisor of Quality Control, you want to test your claim at the 5% significance level. You measure 40 toys and obtain a mean length of 9.45 inches. Alpha = .05.

a. State the question you would like to answer, your null and alternative hypotheses

b. Calculations: Include z score and p-value

c. Conclusion: Rejection decision, why, and answer to the question.

Answer 1

(a) Question: New elves are producing toys that are less than 10 inches.

The hypothesis being tested is:

H₀: µ = 10

H_a: µ < 10

(b) The test statistic, z = (x - µ)/σ/√n

z = (9.45 - 10)/0.3/√40

z = -11.60

The p-value is 0.0000.

(c) Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that new elves are producing toys that are less than 10 inches.

Please give me a thumbs-up if this helps you out. Thank you!