An all-women\'s college is interested in whether it places more females in male-

Question

An all-women's college is interested in whether it places more females in male-dominated careers (e.g., engineering, physical science) than is reflected in the national data for career placement. According to some statistics from the National Center for Educational Statistics, only around 22% of people in engineering and physical science jobs were females in the 1990s (see Bona, Kelly & Jung, 2011, who published about this topic in the Psi Chi journal, if you are interested in this topic). For this problem, assume that figure has remained constant over time. You examine your alumni data, which simply includes annual averages over the past 20 years, (N = 20), and find that on average, 23.7% of graduates have been placed in such occupations, with a standard deviation of 6.1%.

(a) Test your hypothesis as a two-tailed test with alpha = .05.

(b) Compute the 95% confidence interval. Do the results from your confidence interval agree with your decision from the hypothesis test? Explain.

(c) Compute the effect size for this analysis and interpret it.

Explanation / Answer

a) H0:mu=0.22

H1:mu>0.22

Perform 1-sample t test(small sample size, n<30 and sample standard deviation is known).

t=(xbar-mu)/(s/sqrt n), wher xbar is sample mean, mu is population mean, s is sample standrad deviation, and n is sample size.

=(0.237-0.22)/(0.061/sqrt 20)

=1.25

The p value is 0.228, the p value is not less than 0.05. Fail to reject H0, not sufficient sample evidence to cocnclud ethta mor efemales are placed in male dominated carrers.

b) The 95% c.i=xbar+-t19,0.05SE(xbar)

=0.237+-2.093*(0.061/sqrt 20)

=0.209 to 0.266

The interval contains mu=0.22, accept H0, that is fail to reject H0.

This agree with previous result.

c) Efffet size, d=(xbar-mu)/s=(0.237-0.22)/0.061=0.279

The interval

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