Answer to Question #345181 in Statistics and Probability for Josh

Question #345181

The leader of the Factory Worker claims that the average pay of factory workers in



Marikina City is less than 500 php. A random sample of 16 factory workers was



interviewed and resulted on the average of 350 php. Using a significance level of



0.05 and standard deviation of 92. Determine if there is sufficient evidence that the



claim is true.

1
Expert's answer
2022-05-27T11:40:06-0400

The following null and alternative hypotheses need to be tested:

"H_0:\\mu\\ge500"

"H_1:\\mu<500"

This corresponds to a left-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 left-tailed test is "z_c = -1.6449."

The rejection region for this left-tailed test is "R = \\{z<-1.6449\\}."

The z-statistic is computed as follows:


"z=\\dfrac{\\bar{x}-\\mu}{\\sigma\/\\sqrt{n}}=\\dfrac{350-500}{92\/\\sqrt{16}}\\approx-6.5217"

Since it is observed that "z=-6.5217<-1.6449=z_c," it is then concluded that the null hypothesis is rejected.

Using the P-value approach:

The p-value is "p=P(z<-6.5217)=0," and since "p= 0<0.05=\\alpha," it is concluded that the null hypothesis is rejected.

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

is less than 500, at the "\\alpha = 0.05" significance level.


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