6 Fancorp a consulting firm claims that less than half of fr

6. Fancorp (a consulting firm) claims that less than half of franchises are owned by husband-wife team. A simple random sample of 30 franchise owners shows that 12 are owned by husband-wife team. Can you conclude Fancorp?s claim at at a= 0.05? (Use p-value approach) [Hint: the hypothesis one wants to reject is usually the null hypothesis and the hypothesis one wants to conclude is usually the alternative hypothesis (research hypothesis)]

Solution

The test hypothesis:

Ho: p=0.5 (i.e. null hypothesis)

Ha: p<0.5 (i.e. alternative hypothesis)

The test statistic is

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

=(12/30-0.5)/sqrt(0.5*0.5/30)

=-1.10

It is a left-tailed test.

So the p-value= P(Z<-1.10) =0.1357 (from standard normal table)

The rejection region is if the p-value is less than the significant level, we reject the null hypothesis.

Since the p-value is larger than 0.05, we do not reject the null hypothesis.

So we can not conclude that Fancorp\' claim is correct