Question

in 2010, 71% of undergraduates attending a large universitity planned to attend graduate school after graduation. In 2015, a SRS of 110 undergraduates found that 71 planned to attend graduate school. Test the claim that the proportion of undergraduates planning to attend graduate school was different in 2015 than in 2010 at the 0.025 level of significance. Formulate the claim. Calculate the test statistic. Find the P-Value. Formulate the conclusion both statistically and practically.

Answer 1

Given: n=110 x=71

The sample proportion , p=x/n=71/110=0.6455

1) Hypothesis :    VS $H_a:P\neq P_0=0.71$

2) The test statistic under Ho is ,

$Z=\frac{p-P_0}{\sqrt{P_0Q_0/n}}\to N(0,1)$

$=\frac{0.6455-0.71}{\sqrt{0.71*0.29/110}}=-1.49$

3) Since , the test is two tailed

P value = $P(Z>|Z_{stat}|)=P(Z>1.49)=2*0.068112=0.1362$

4) Decision : Here , P value = 0.1362> $\alpha$ =0.025

Therefore , fail to reject Ho at 0.025 significance level

5) Conclusion : Hence , there is not sufficient evidence to conclude that the proportion of undergraduates planning to attend graduate school was different in 2015.