Question

An opinion poll asks a simple random sample of 100 college seniors how they view their job prospects. In all, 53 say "good." Does the poll give convincing evidence to conclude that more than half of all seniors think their job prospects are good? If p = the proportion of all college seniors who say their job prospects are good, what are the the hypotheses for a test to answer this question?

Answer 1

Answer:

We are tryng to proof if more than half of all seniors think their job prospects are good so that would be the alternative hypothesis and the complement rule would be the null hypothesis.:  

Null hypothesis:$p\leq 0.5$  

Alternative hypothesis:$p > 0.5$  

Step-by-step explanation:

Information provided

n=100 represent the random sample ofcollege senior selected

X=53 represent the college seniors who say good

$\hat p=\frac{53}{100}=0.53$ estimated proportion of seniors who think their job prospects are good

$p_o=0.5$ is the value that we want to test

z would represent the statistic

$p_v$ represent the p value

System of hypothesis

We are tryng to proof if more than half of all seniors think their job prospects are good so that would be the alternative hypothesis and the complement rule would be the null hypothesis.:  

Null hypothesis:$p\leq 0.5$  

Alternative hypothesis:$p > 0.5$  

The statistic is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)  

Replacing the info given we have:

$z=\frac{0.53 -0.5}{\sqrt{\frac{0.5(1-0.5)}{100}}}=0.6$  

The p value for this case would be given by

$p_v =P(z>0.6)=0.274$