Question

We want to be rich In a recent year, $73\%$of first-year college students responding to a national survey identified “being very well-off financially” as an important personal goal. A state university finds that $132$of an SRS of $200$of its first-year students say that this goal is important. Is there convincing evidence at the $\alpha =0.05$significance level that the proportion of all first-year students at this university who think being very well-off is important differs from the national value of 73%?

Short answer

There is sufficient evidence present to show that students of the view that well off is different from national value.

Step-by-step solution

Given Information

It is given that $\text{Hypothesized proportion}\left(p_o\right)=73\%=0.73$

$\left(\hat{p}\right)=\frac{132}{200}=0.66$

$\left(\alpha \right)=0.05$

Calculation and Explanation

Null hypothesis: $H_0:p_0=0.73$

Alternative hypothesis: $H_a:p_0\ne 0.73$

Output of MINTAB is:

Here, $P\mathrm{value}<\mathrm{\alpha }$, null hypothesis is rejected.

Hence, sufficient evidence is present to conclude at $5\%$level of significance that well off is different from national value.