Hypothesis Testing

Hypothesis Testing

Student’s Name

Institution Affiliation

Course Name and Code

Professor’s Name

Date

Hypothesis Testing

The null and alternative hypotheses

The parameter of interest here is the population mean (µ), which is the diameter of part produced by a test run. The null hypothesis, the mean diameter of parts produced by a test run is equal to 6 inches, is represented by H0, while the alternative hypothesis, diameter of parts produced by a test run is not equal to 6 inches, is represented by H1. Thus;

H0: µ = 6 inches

H1: µ ≠ 6 inches

The decision rule assuming that n = 200 and α = 0.01

Because the sample size (n=200) is sufficiently larger, by Central Limit Theorem (CLT), the sample mean follows a normal distribution. Therefore, the decision rule holds that reject H0 if ∣z∣>zα/2. Since the level of significance (α) = 0.01, we use excel to find z0.005.

z0.005. = 2.575829304.

Thus, the decision rule is as follows:

Reject H0 if z < -2.575829304 or z > 2.575829304; where z is the test statistic.

What the Lazer Company should conclude if the sample mean diameter for the 200 parts is 6.03 inches.

z = xˉ- µẟn,

Where;

xˉ – Sample mean

µ- population mean

ẟ – Standard deviation

n – Sample size

z = 6.03- 60.1200,

From excel, z= 4.242640687

Recommendation

Based on the earlier developed decision rule, we reject H0 since |z = 4.242640687| > 2.575829304. At 0.01 significance level, there is sufficient evidence to conclude that the mean diameter of part for Boeing Corporation produced by the test run is not equal to 6 inches. Thus, the Lazer Company should conclude that the mean diameter of a part of Boeing Corporation from the test run differs from the contract’s requirement.