Assume all populations are normally distributed, all samples are randomly select

Question

Assume all populations are normally distributed, all samples are randomly selected. find z or t which ever is appropiate. Draw, labal, and shade a curve showing the region of rejection. Identifiy critical values or p-values, whichever one you are using. Tell whther you reject or fail to reject the null hypothesis and why, and interpret your decision.

An employment information service claims the mean annual salary for full-time female workers ove the age of 25 and without a high school diploma is 21,000. The mean annual salary for a random sample of 12 full-time female workers over the age of 25 without a high school diploma is 20,086.50, with a standard deviation 1417.14 At a=.10, is there enough evidence to reject the claim?

Explanation / Answer

Hypothesis:

H0 ; mu = 21000

Ha: mu not equal to 21000

Test statistic:

n = 12 , s = 1417. 14 , x = 20086.50

t = ( x - mean) / ( s / sqrt(n))

= ( 20086.50 - 210000) / ( 1417.14 / sqrt(12))

= -2.23

Now, we need to find p value using t = -2.23 with df = 11

p value = .047526.

As p value is less than significance level 0.10 , So, we reject the null hypothesis

there is enough evidence to reject the claim

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