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.

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

INFO:

z-test hypothesis test for population mean

test-statistic = 3.32

two tailed p-value = 0.0009

90% confidence interval (rounded) = (2.41, 2.65)

99% confidence interval (rounded) = (2.35, 2.71)

Thank you!

Answer 1

Given from previous studies that the average diameter of ball bearings from this manufacturing process is 2.30 cm.

let be the population mean diameter of ball bearings

Null Hypothesis H₀ : 2.30 ( The mean diameter of the ball bearings are less than or equal to 2.30 cm)

Alternative Hypothesis H₁ : > 2.30 cm ( The mean diameter of the ball bearings are more than to 2.30 cm)

level of significance alpha = 0.01 , one tail test

given Z-test statistic = 3.32

p-value = 0.00045

since the p-value is less than alpha (0.05) we reject the null hypothesis and conclude that the average diameter is greater than 2.30 cm.