Assume that the two samples are independent simple random samples selected from
ID: 3237227 • Letter: A
Question
Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Statistics from the ages of unsuccessful and successful applicants for a promotion are given below. Treat the data as samples from larger populations and use a 0.05 significance level to test the claim that the unsuccessful applicants are from a population with a greater mean age than the mean age of successful applicants. Based on the result, does there appear to be discrimination based on age? Ages of unsuccessful applicants n = 23, x bar = 50.0 years, s = 7.9 years Ages of successful applicants n = 30, x bar = 42.1, years, s = 5.1 years H_0 There sufficient evidence that the unsuccessful applicants are from a population with a greater mean age than the mean age of successful applicants. Based on the result, does there appear to be discrimination based on age? there appear to be discrimination based on age.Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: Unsuccessful< Successful
Alternative hypothesis: Unsuccessful > Successful
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 1.892
DF = 51
t = [ (x1 - x2) - d ] / SE
t = 4.18
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
The observed difference in sample means produced a t statistic of 4.18. We use the t Distribution Calculator to find P(t > 4.18) = 0.000057
Interpret results. Since the P-value (0.000057) is less than the significance level (0.05), we have to reject the null hypothesis.
Reject H0, From the above test we have sufficient evidence in the favor of the claim that unsuccessful applicants are from population with greater mean age than the mean age of successful apllicants.
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