Answer :
Answer: Yes
Step-by-step explanation:
As per the given information, we have to test the hypothesis:
[tex]H_0:p=0.57\\\\ H_a:p\neq0.57[/tex] , where p = Population proportion of college students work year-round.
Since the alternative hypothesis is two-tailed , so test is a two-tailed test.
In a random sample of 300 college students, 171 say they work year-round.
⇒ sample size : n= 300
⇒ sample proportion : [tex]\hat{p}=\dfrac{171}{300}=0.57[/tex]
Test statistics : [tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]
[tex]z=\dfrac{0.57-5.57}{\sqrt{\dfrac{0.57(1-0.57)}{300}}}\\\\=0[/tex]
P-value = 2P(Z>|z| = 2P(Z>|0|))
=2P(Z>0) = 2(1-P(Z<0)) [∵ P(Z>z)=1-P(Z<z)]
=2(1-0.50) [ By z-table]
=1.00
Decision : P-value(1.00) > Significance level (0.10) , it means we cannot reject the null hypothesis.
We conclude that there is enough evidence to support researcher's claim that 57% of college students work year-round.