You survey 300 people and find that 80 of them do not have s

You survey 300 people and find that 80 of them do not have siblings. Is this significantly different from the 25% know for the US average? Find the z* value that you will use to test this question. give your answer as 0.XX

The alternate Hypothesis is: left tailed, right tailed, two tailed, or none of the above

Solution

Null hypothesis: p=0.25

Alternative hypothesis: p not equal to 0.25 (i.e. two tailed)

The test statistic is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(80/300-0.25)/sqrt(0.25*0.75/300)

=0.67

Assume that the significant level a=0.05

The critical values are Z(0.025) = -1.96 or 1.96 (from standard normal table)

The rejection regions are if Z<-1.96 or Z>1.96, we reject the null hypothesis.

Since Z=0.67 is between -1.96 and 1.96, we do not reject the null hypothesis.

So we can not conclude that this is significantly different from the 25% know for the US average