A study was conducted to examine the proportion of children

A study was conducted to examine the proportion of children in grades K-4 who eat breakfast before coming to school. A random sample of 500 children in grades K-4 was obtained, and interviews with the children were used to determine that 325 had breakfast before coming to school. Is there any evidence to suggest that the true population proportion of children in grades K-4 who eat breakfast before coming to school is less than 0.67?

Solution

Ho: p=0.67 (i.e. null hypothesis)

Ha: p<0.67 (i.e. alternative hypothesis)

The test statistic is

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

=(325/500-0.67)/sqrt(0.67*(1-0.67)/500)

=-0.95

It is a left-tailed test.

Assume that the significant level a=0.05

The critical value is Z(0.05) = -1.645 (from standard normal table)

The rejection region is if Z<-1.645, we reject the null hypothesis.

Since Z=-0.95 is larger than -1.645, we do not reject the null hypothesis.

So we can not conclude that the true population proportion of children in grades K-4 who eat breakfast before coming to school is less than 0.67