Question

An all-women's college is interested in knowing 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 the National Center for Educational Statistics, only around 22% of the people in engineering and physical science jobs were females in the 1990s. For this problem, assume that this figure has remained constant over time. Over the past 20 years (N = 20), 23.7% of female graduates have been placed in such occupations on average, with a standard deviation of 6.1%. (a) Compute the t statistic. (b) Assess your hypothesis as a two-tailed test with p = .05. (c) Compute the effect size for this analysis and explain what this effect size means.

Answer 1

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+-t_19,0.05SE(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