Question

It has been claimed from previous studies that the average diameter of ball bearings from this manufacturing process is 2.30 cm. Based on the sample of 50 that you collected, is there evidence to suggest that the average diameter is greater than 2.30 cm? Perform a hypothesis test for the population mean at alpha = 0.01.

a. Define the null and alternative hypothesis for this test in mathematical terms and in words.
b. Report the level of significance.

Answer 1

The null hypothesis (H0) for a hypothesis test on the average diameter of ball bearings is μ = 2.30 cm, and the alternative hypothesis (H1) is μ > 2.30 cm. The test is performed at a level of significance of α = 0.01, indicating a 1% risk of a Type I error.

Step-by-step explanation:

Understanding Hypothesis Testing

To perform a hypothesis test for the population mean where it is claimed that the average diameter of ball bearings is greater than 2.30 cm, we need to define the null and alternative hypotheses and report the significance level.

a. In mathematical terms, the null hypothesis (H0) and the alternative hypothesis (H1) can be set up as follows:

H0: μ = 2.30 cm (The population mean diameter is 2.30 cm)

H1: μ > 2.30 cm (The population mean diameter is greater than 2.30 cm)

In words, the null hypothesis states that the mean diameter of the ball bearings is equal to 2.30 cm, and the alternative hypothesis posits that the mean diameter is greater than 2.30 cm.

b. The level of significance (α) is the probability of making a Type I error (rejecting the null hypothesis when it is actually true). For this test, the level of significance is set at α = 0.01, meaning there is a 1% chance of incorrectly rejecting the null hypothesis if it is true.