Hypothesis Testing

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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.