it is claimed that the average monthly income of chemical engineers last year was P27,900.00 A random sample of 36 chemical engineers is selected and it is found out that the average monthly salary is P28,000.00 Using a 0.05 level of significance can it be concluded that there is an increase in the average monthly income of chemical engineers? Assume that the population standard deviation is P250.50
The following null and alternative hypotheses need to be tested:
"H_0:\\mu\\le40"
"H_1:\\mu>40"
This corresponds to a right-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 right-tailed test is "z_c = 1.6449."
The rejection region for this right-tailed test is "R = \\{z:z>1.6449\\}."
The z-statistic is computed as follows:
Since it is observed that "z=2.3952>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>2.3952)= 0.008306," and since "p= 0.008306<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 greater than 27900.00, at the "\\alpha = 0.05" significance level.
Comments
Leave a comment