An all-women’s college is interested in knowing whether it places more or less f

Question

An all-women’s college is interested in knowing whether it places more or less females in male-dominated careers (e.g., engineering, physical science) as compared to 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 population parameter has remained constant over time. The alumni data at this all-women’s college has observed the percent of graduates placed in such occupations over the past 20 years (N = 20). The mean for those years is 23.7% with a standard deviation of 6.1%. Test the hypothesis that the women’s college average is different from the national average. Complete the following steps to test this hypothesis using alpha = .05.

a. What are the hypotheses in formal statistical notation?

b. Compute the 95% confidence interval and report it using correct notation.

c. Make a decision regarding the null hypothesis. How did you reach this decision using the confidence interval? Explain what you would conclude about the research question.

Explanation / Answer

a) H0: = 0.22

H1: > 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

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

If the confidence interval does not contain the null hypothesis value, the results are statistically significant.

Here, null value is contained in interval

This agrees with previous result. Thus,

Fail to reject H0, not sufficient sample evidence to cocnclud ethta mor efemales are placed in male dominated carrers.

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