A congressman decides to vote for a bill that he personally

A congressman decides to vote for a bill that he personally opposes if more than 60% of his constituents favor the bill. In a survey of 200 randomly selected voters in the congressman

Solution

The test hypothesis:

Ho: p=0.6 (i.e. null hypothesis)

Ha: p not equal to 0.6 (i.e. alternative hypothesis)

The test statisitc is

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

=(140/200-0.6)/sqrt(0.6*0.4/200)

=2.89

It is a two-tailed test.

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=2.89 is larger than 1.96, we reject the null hypothesis.

So we can conclude that the percent of constituents favoring the bill is different than 60%