An employment information service claims the mean annual pay for full-time male

Question

An employment information service claims the mean annual pay for full-time male workers over age 25 without a high school diploma is $22, 275. The annual pay for a random sample of 10 full-time male workers over age 25 without a high school diploma is listed. At alpha = 0.05, test the claim that the mean salary is $22, 275. Assume the population is normally distributed. 20, 653 21, 136 22, 351 21, 393 22, 972 16, 917 19, 153 23.191 24, 187 26, 284 (a) Write the claim mathematically and identify H_0 and H_a. Which of the following correctly states H_0 and H_a? A. H_0: mu > 22, 275 H_a: mu lessthanorequalto 22, 275 B. H_0: mu = 22, 275 H_a: mu > 22, 275 C. H_0: mu = 22, 275 H_a: mu

Explanation / Answer

Solution:-

The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: = 22,275
Alternative hypothesis: 22,275

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n) = 2628.538379235 / sqrt(10) = 831.216819555
DF = n - 1 = 10 - 1 = 9
t = (x - ) / SE = (21823.7 - 22275)/831.216819555 = -0.5429

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the t statistic having 9 degrees of freedom is less than -0.5429 or greater than 0.5429.

We use the t Distribution Calculator to find P(t < -0.5429), and P(t > 0.5429)

The P-Value is 0.600317.
The result is not significant at p < 0.05

Interpret results. Since the P-value (0.600317) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Conclusion. Fail to reject the null hypothesis. We have sufficient evidence to prove the claim, that the mean annual pay for full time male workers over age 25 without a high school diploma is $22,275.

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