Your next task is to examine whether there is a significant racial/ethnic differ

Question

Your next task is to examine whether there is a significant racial/ethnic difference in the average number of college-level science course taken among Americans who have taken at least one-college level science course. Descriptive results for Americans with more than 12 years of schooling who have taken at least one college-level science course are as follows: White Americans (N = 271) have a mean of 7.54 and a standard deviation of 10.37, and Black/Latinx Americans (N = 77) have a mean of 4.73 and standard deviation of 5.26.

a. Identity the research and null hypotheses for a hypothesis test of difference between White Americans and Black/Latinx Americans in the average number of college-level science course taken.

b. Identify the critical value for an alpha of .05.

c. Calculate the difference between White Americans and Black/Latinx Americans in the average number of college-level science course taken.

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 who have taken at least one college-level science course.

Explanation / Answer

Part-a

Null hypothesis H0: µ1= µ2

Alterative hypothesis Ha: µ1 µ2

Here µ1 and µ2 are the true average number of college-level science course for White Americans and Black/Latinx Americans respectively.

Part-b

We are given

White Americans : Sample mean xbar1=7.54, standard deviation s1=10.37 and sample size n1=271

Black Americans : Sample mean xbar2=4.73, standard deviation s1=5.26 and sample size n1=77

So, degree of freedom =n1+n2-2=271+77-2=346

Two tailed Critical t=±1.9668

Part-c

Difference between White Americans and Black/Latinx Americans in the average number of college-level science course taken=7.54-4.73=2.81

Part-d

Standard error of difference= sqrt( (n1-1)*s12+(n2-1)*s22)/(n1+n2-2))*sqrt(1/n1+1/n2)

=sqrt(271-1)*10.372+(77-1)*5.262)/(271+77-2))*sqrt(1/271+1/77)

=1.23

Part-e

Test statistic t=Mean difference /SE

=2.81/1.23

=2.28

Part-f

As calculated>1.9668(critical t), so we reject the null hypothesis. This means that there is significant difference in difference between White Americans and Black/Latinx Americans in the average number of college-level science course taken.

Part-g

We found that the race affects the average number of college-level science course taken. Also, the average number of college-level science course taken by white Americans is higher than that of Black Americans indicating that the white race is more inclined towards science.

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