Answer to Question #342403 in Statistics and Probability for gel

Question #342403

A chemical company alleged that the average weight of the bag of chemical is 30kgs. with a standard deviation of 1.1 kgs. A sample of 26 bags was taken and revealed a mean weight of 28.9 kgs. Shall we accept the allegation of the chemical company? Use .01 level of significance



1
Expert's answer
2022-05-20T08:13:17-0400

The following null and alternative hypotheses need to be tested:

"H_0:\\mu=30"

"H_1:\\mu\\not=30"

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 = 0.01," and the critical value for a two-tailed test is "z_c = 2.5758."

The rejection region for this two-tailed test is "R = \\{z:|z|>2.5758\\}."

The z-statistic is computed as follows:


"z=\\dfrac{\\bar{x}-\\mu}{\\sigma\/\\sqrt{n}}=\\dfrac{28.9-30}{1.1\/\\sqrt{26}}\\approx-5.09902"

Since it is observed that "|z|=5.09902>2.5758=z_c," it is then concluded that the null hypothesis is rejected.

Using the P-value approach:

The p-value is "p=2P(z<-5.09902)=0," and since "p= 0<0.01=\\alpha," it is concluded that the null hypothesis is rejected.

Therefore, there is enough evidence to claim that the population mean "\\mu"

is different than 30, at the "\\alpha = 0.01" significance level.



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