According to an Experiential Education Survey published at JobWeb.com, the avera

Question

According to an Experiential Education Survey published at JobWeb.com, the average hourly wage of a college student working as a co-op is $15.64 an hour and the average hourly wage of an intern is $15.44. The sample standard deviation of co-op students and interns are 1.05 and 0.92 respectively. We collect 12 co-op students and 12 interns in the samples. (1). Assume that such wages are normally distributed in the population and that the population variances are equal. Use these data and a = .10 to manually test and determine if there is a significant difference in the mean hourly wage of a college co-op student and the mean hourly wage of an intern.

Explanation / Answer

We will be conducting two-sample t-test, because the following conditions (assumptions) are met:

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

Null hypothesis: There is no significant difference between average hourly wage of a college student working as a co-op and the average hourly wage of an intern. That is, 1 - 2 = 0
Alternative hypothesis: There is significant difference between average hourly wage of a college student working as a co-op and the average hourly wage of an intern. That is,1 - 2 0

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

Formulate an analysis plan. For this analysis, the significance level is 0.10. 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 = sqrt[(1.052/12) + (0.922/12] = 0.403

DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] }

= (1.052/12 + 0.922/12)2 / { [ (1.052 / 12)2 / (12 - 1) ] + [ (0.922 / 12)2 / (12 - 1) ] }

= 22 (Rounding to nearest integer)

t = [ (x1 - x2) - d ] / SE = (15.64 - 15.44) / 0.403 = 0.4963

P-value for t = 0.4963 and degree of freedom = 22 is 0.3123

For two-tail test, P-value = 2 * 0.3123 = 0.6246

Interpret results. Since the P-value (0.6246) is greater than the significance level (0.10), we accept the null hypothesis and conclude that there is no significant difference between average hourly wage of a college student working as a co-op and the average hourly wage of an intern.

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