Lock, Statisticss Unlocking the Power of Data, 2e Help PRINTER VERSION ·BACK Cha

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Lock, Statisticss Unlocking the Power of Data, 2e Help PRINTER VERSION ·BACK Chapter 6, Section 4-HT, Exercise 216 Is Gender Bias Influenced by Facuity Gender? In a study' examining gender bias, a nationwide sample of 127 science professors evaluated the application materials of an undergraduate student who had ostensibly applied for a laboratory manager position. Ail the faculty members received the same application, with half randomly given a male name and half randomly given a female name. We see that the applications sigrificanty with female names, is the mean recommended salary different depending on the gender of the evaluating faculty member? The 32 male with female names received a faculty gave a mean starting salary of $27,111 with a standard deviation of $6948 while the 32 female faculty gave a mean starting salary of $25,000 with a standard deviation of $7966. Let oroup 1 and group 2 be the salary recommended for female applicants by male faculty members and female facuity members, respectively Moss Racusin, CA,taience faculty's subtle gender biases favor male students, Proceedings of the kstional Academy of Sciences, State the null and alternative hypotheses 7 shift

Explanation / Answer

Null and alternative hypothesis is,

H0: 1 = 2
Ha: 1 2

For this analysis, we assume the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

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)]

where s1 is the  standard deviation of group 1, s2 is the standard deviation of group 2, n1 is the size of group 1, n2 is the size of group 2, x1 is the mean of group 1, x2 is the mean of group 2, and SE is the standard error.

SE = sqrt[(69482/32) + (79662/32] = 1868.588

DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] }
DF = (69482/32 + 79662/32)2 / { [ (69482 / 32)2 / (31) ] + [ (79662 / 32)2 / (31) ] }

= 60.876 = 61 (Rounding to next integer)

Test Statistic t = [ (x1 - x2) ] / SE = [ (27111 - 25000) ] / 1868.588 = 1.1297

Test Statistic t = 1.130

Since we have a two-tailed test, the P-value is the probability that a t statistic having 61 degrees of freedom is more extreme than 1.1297; that is, less than -1.1297 or greater than 1.1297.

We use the t Distribution Calculator to find P(t < -1.1297) = 0.1315, and P(t > 1.1297) = 0.1315. Thus, the P-value = 0.1315 + 0.1315 = 0.263

So, p-value = 0.263

Since the P-value (0.263) is greater than the significance level (0.05), we do not reject the null hypothesis.

There is no evidence that to comclude that mean recommended salary is different depending on the gender of the evaluator. The answer is NO

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