Question

ZIPPY MOTORS and the EPA The EPA questions the report it received from the Zippy Motor Company. The Zippy Company claimed that the motors it has produced are in compliance with the EPA maximum noise emission of 15dB.

Zippy has produced 867 motors and cannot ship them until they are approved by the EPA for noise level compliance. Rather than test each one, they have tested two random samples with results as follows:

Sample A

Size 32

Mean 14.9 dB

Sample B

Size 34

Mean 14.7 dB

The EPA examined several motors and doubted the validity of Zippy’s tests, so it tested the entire lot with the following results: Entire Lot Size 867 Mean 15.6 dB Std Dev 0.6 dB

What is the likelihood of the results of the two random samples reported by Zippy? What do you suspect Zippy did to obtain those results?

Find the probability and z score for Sample A and Sample B.

Answer 1

Here we have

Hypothese are:

Sample A:

Here we have

The test statistics is

Test is right tailed.

Using excel function "=1-NORMSDIST(-0.97)" the p-value of the test is

p-value = 0.8264

Decision:

Since p-value is greater than 0.05 so we fail to reject the null hypothesis.

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Sample B:

Here we have

The test statistics is

Test is right tailed.

Using excel function "=1-NORMSDIST(-2.92)" the p-value of the test is

p-value = 0.9982

Decision:

Since p-value is greater than 0.05 so we fail to reject the null hypothesis.