“Would you marry a person from a lower social class than your own?” Researchers asked this question of a random sample of black, never married students at two historically black colleges in the South. Of the men in the sample, said “Yes.” Among the women, said “Yes.”Is there reason to think that different proportions of men and women in this student population would be willing to marry beneath their class?
Holly carried out the significance test shown below to answer this question. Unfortunately, she made some mistakes along the way. Identify as many mistakes as you can, and tell how to correct each one.
State: I want to perform a test of
at the confidence level.
Plan: If conditions are met, I’ll do a one-sample test for comparing two proportions.
- Random The data came from a random sample of 385 black, never-married students.
- Normal One student’s answer to the question should have no relationship to another student’s answer.
- Independent The counts of successes and failures in the two groups, and are all at least
Do: From the data, and .
Test statistic
=value From Table A, role="math" localid="1650292307192" .
Conclude: The -value, , is less than , so I’ll reject the null hypothesis. This proves that a higher proportion of men than women are willing to marry someone from a social class lower than their own.
