Question

The data colleted was from 50 random samples. Out of these half were college graduates and half were high school graduates. There are a few things that we can infer from this data. Car ownership was roughly the same between both groups (60% college grads; 56% highschool grads). Home ownership was noticeably higher in college graduates, with only 32% of high school grads owning a home and 56% of college graduates. This may be attributed to the different in salary mean between both groups, $37871.36 for high school and $76,154.40 for college. Although the college group had obviously higher education debts, it can be inferred that college graduates are making up for this loss with a yearly salary gain of an average of $38,283.04 above the high school graduate mean.

The mean salary of college graduates was $76,154.40 with a standard diviation of 54501.758. The proportion of graduates with a debt exceeding $30,000 was .28, or 28% of the graduates sampled.$37,871.36

1. Use your sample data to construct and interpret confidence intervals for each statistic:
   • For the PROPORTION:
     • Construct and interpret a 90% confidence interval for the population proportion.
     • What sample size would be necessary to estimate the proportion with a 2% margin of error and a 90% confidence? (Use formula found in Chapter 8 and/or technology)
   • For the MEAN:
     • Construct and interpret a 95% confidence interval for the population mean.
     • Do you think that your sample of size 50 is large enough? Why or why not?

Answer 1

For proportion

p=0.28, N=50

For Mean

The sample size is moderately large. A sample size of 100 could have been better but the sample size of 30 or more is relatively better.