A placement office at a large university claims that approximately $70 \%$ of the school's graduates will obtain jobs in their major field upon graduation. The administration feels that the percentage is larger than $70 \%$. From a random sample of 100 recent graduates it was found that 75 had obtained jobs in their field. The hypotheses are A) $H_{0}: p_{1}-p_{2}=0.70$ $H_{\mathrm{A}}: p_{1}-p_{2}0.70$ B) $H_{0}: p=0.70$ $H_{\mathrm{A}}: p0.70$ C) $H_{0}: p

Question

A placement office at a large university claims that approximately $70 \%$ of the school's graduates will obtain jobs in their major field upon graduation. The administration feels that the percentage is larger than $70 \%$. From a random sample of 100 recent graduates it was found that 75 had obtained jobs in their field. The hypotheses are
A) $H_{0}: p_{1}-p_{2}=0.70$
$H_{\mathrm{A}}: p_{1}-p_{2}>0.70$
B) $H_{0}: p=0.70$
$H_{\mathrm{A}}: p>0.70$
C) $H_{0}: p<0.70$
$H_{\mathrm{A}}: p \geq 0.70$
D) $H_{0}: p=0.70$
$H_{\mathrm{A}}: p \neq 0.70$

Quizplus · Accepted Answer

The correct hypothesis testing setup for this scenario is $H_{0}: p=0.70$ against $H_{\mathrm{A}}: p>0.70$, where $p$ represents the proportion of graduates obtaining jobs in their field. The null hypothesis states the claim to be tested (that the proportion is 70%), and the alternative hypothesis reflects the administration's belief that the proportion is greater than 70%.

A Placement Office at a Large University Claims That Approximately 70%70 \%70%

A Placement Office at a Large University Claims That Approximately $70 \%$