Answer to Question #215644 in Mechanical Engineering for J MAYAKAYAKA

Question #215644

A melting point test ofinwant to test the claim that the temperature is different fromx D154:2 F. Assume that the melting point is normally distributed withn D10 samples of a binder used in manufacturing a rocket propellant resulted155 F: Test the hypothesis atD1:5 F: Suppose youD0:05:

1
Expert's answer
2021-07-12T03:36:24-0400

The following null and alternative hypotheses need to be tested:

"H_0:\\mu=155"

"H_1:\\mu\\not=155"

​This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation, will be used.

Based on the information provided, the significance level is "\\alpha=0.05," and the critical value for a two-tailed test is "z_c=1.96."

The rejection region for this two-tailed test is"R=\\{z:|z|>1.96\\}."

The z-statistic is computed as follows:



"z=\\dfrac{\\bar{x}-\\mu}{\\sigma\/\\sqrt{n}}=\\dfrac{154.2-155}{1.5\/\\sqrt{10}}""\\approx-1.686548"

Since it is observed that "|z|=1.686548<1.96=z_c," it is then concluded that the null hypothesis is not rejected.

Using the P-value approach:

The p-value is "p=2P(Z<-1.686548)=0.09169," and since "p=0.09169>0.05=\\alpha," it is concluded that the null hypothesis is not rejected.

Therefore, there is not enough evidence to claim that the population mean "\\mu"

is different than 155, at the "\\alpha=0.05" significance level.


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