Let’s say you are interested in promoting more race conscious science curriculum
ID: 3223045 • Letter: L
Question
Let’s say you are interested in promoting more race conscious science curriculum at UT. In order to build a case for your campaign, you decide to examine racial differences in college-level science course taking using the 2012 GSS data. Your first task is to examine whether Black/Latinx Americans are significantly more or less likely to take at least one college-level science class than White Americans. Descriptive results show that 74.3% of White Americans (N = 378) with more than 12 years of schooling have taken at least one college-level science class compared to 59.8% of Black/Latinx Americans (N = 132) with more than 12 years of schooling.
a. Identity the research and null hypotheses for a hypothesis test of difference between White Americans and Black/Latinx Americans in the likelihood of taking college-level science.
b. Identify the critical value for an alpha of .05.
c. Calculate the difference between White American and Black/Latinx Americans in the likelihood of taking college-level science.
d. Calculate the standard error of the difference.
e. Calculate the test statistic of the difference.
f. Based on your results, identify whether you reject or fail to reject the null hypothesis. What does this mean?
g. Write a 2-3 sentence interpretation of the relationship between race/ethnicity and science course taking among Americans with more than 12 years of education.
Explanation / Answer
a. Null Hypothesis : H0: There is no difference between whit Americans and Black/ Latin Americans in the likelihood of taking college level science. pWhite- pblack=0
Alternative Hypothesis : Ha : There is significant difference between White Americans and Black/ Latin Americans in taking college level science. pWhite- pblack >=0
b. Critical value for alpha = 0.05
Zcritical = +-1.96
c. the difference between White American and Black/Latinx Americans in the likelihood of taking college-level science = 0.743 - 0.598 = 0.145 = 14.5 %
d. standard error of the difference =?
pooled estimate of p = p* = (n1p1+ n2p2)/(n1+ n2) = (0.743 * 378 + 0.598 * 132)/ ( 378 + 132) = 0.7055
and standard error of the difference SE0= sqrt [ p* (1- p*) (1/n1+1/n2)]
= sqrt [ 0.7055 * 0.2945 * ( 1/378 + 1/132)]
= 0.0461
e. . test statistic of the difference
Z = (p1- p2)/ SE0= (0.743 - 0.598)/ 0.0461 = 3.145
f. Based on the results, Z > Zcritical , we can reject the null hypothesis and can conclude that there is significant difference between White Americans and Black/ Latin Americans in taking college level science.
g. In US, by this study we can see that there is significant difference between white and black/ Latin people in taking science course with more than 12 years of education. Black are more prone to take commerce and humanity subjects. It is may be because high fees of science courses in US.
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