In a recent year, 73% of first-year college students responded to a national survey and identified "being very well-off financially" as an important personal goal. A state university finds that 132 of a simple random sample of 200 of its first-year students say that this goal is important.
a) Give a 95% confidence interval for the proportion of all first-year students at the university who would identify being well-off as an important goal. Keep 4 decimal places.
[0.63, 0.71]
b) Is there good evidence that the proportion of all first-year students at this university who think being well-off is important DIFFERS FROM the national value, 73%? Check to make sure you can safely use the methods discussed in this section of your book. State the hypotheses, give a test statistic, find the P-value, and state your conclusions. For the first blank in each hypothesis use one of the following terms: equal to, not equal to, greater than, greater than or equal to, less than, or less than or equal to.
H0: p = 0.73
Ha: p ≠ 0.73
z Test Statistic = -1.33
p-value = 0.183
Conclusion at 5% level of significance: Do not reject H0.