Chapter 6, Section 4-HT, Exercise 215 - MathPad Gender Bias In a study1 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. All participants received the same materials, which were randomly assigned either the name of a male (nm=63) or the name of a female (nf=64). Participants believed that they were giving feedback to the applicant, including what salary could be expected. The average salary recommended for the male applicant was $30,238 with a standard deviation of $5152 while the average salary recommended for the (identical) female applicant was $26,508 with a standard deviation of $7348. Does this provide evidence of a gender bias, in which applicants with male names are given higher recommended salaries than applicants with female names? Let group 1 and group 2 be the salary recommended for male applicants and female applicants, respectively. 1Moss-Racusin, C.A., et al., “Science faculty’s subtle gender biases favor male students,” Proceedings of the National Academy of Sciences, 109(41), October 9, 2012, 16764–479. State the null and alternative hypotheses. Your answer should be an expression composed of symbols: =,≠,<,>,μ,μ1,μ2,p,p1,p2,ρ,p^,p^1,p^2,r. H0: vs Ha:Edit Calculate the relevant test statistic. Round your answer to three decimal places. t-statistic = Enter your answer in accordance to the question statement the absolute tolerance is +/-0.02 Find the p-value. Round your answer to four decimal places. p-value = Enter your answer in accordance to the question statement the absolute tolerance is +/-0.0008 What is the conclusion? Reject H0. Do not reject H0.

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Chapter 6, Section 4-HT, Exercise 215 - MathPad

Gender Bias

In a study¹ 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. All participants received the same materials, which were randomly assigned either the name of a male (nm=63) or the name of a female (nf=64). Participants believed that they were giving feedback to the applicant, including what salary could be expected. The average salary recommended for the male applicant was $30,238 with a standard deviation of $5152 while the average salary recommended for the (identical) female applicant was $26,508 with a standard deviation of $7348. Does this provide evidence of a gender bias, in which applicants with male names are given higher recommended salaries than applicants with female names?

Let group 1 and group 2 be the salary recommended for male applicants and female applicants, respectively.

¹Moss-Racusin, C.A., et al., “Science faculty’s subtle gender biases favor male students,” Proceedings of the National Academy of Sciences, 109(41), October 9, 2012, 16764–479.

State the null and alternative hypotheses. Your answer should be an expression composed of symbols: =,≠,<,>,μ,μ1,μ2,p,p1,p2,ρ,p^,p^1,p^2,r.

H0: vs Ha:Edit

Calculate the relevant test statistic.

Round your answer to three decimal places.

t-statistic = Enter your answer in accordance to the question statement

the absolute tolerance is +/-0.02

Find the p-value.

Round your answer to four decimal places.

p-value = Enter your answer in accordance to the question statement

the absolute tolerance is +/-0.0008

What is the conclusion?

Reject H0.

Do not reject H0.

Do we have evidence to conclude that applicants with male names are given higher recommended starting salaries than applicants with female names?

Yes

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