Yes because the test value 064 is in the noncritical region

Yes, because the test value 0.64 is in the noncritical region.

No, because the test value 0.70 is in the critical region.

Yes, because the test value 0.70 is in the noncritical region.

No, because the test value 0.64 is in the noncritical region.

Solution

The test hypothesis:

Ho: p=0.65 (i.e. null hypothesis)

Ha: p not equal to 0.65 (i.e alternative hypothesis)

The test statistic is

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

=(38/55-0.65)/sqrt(0.65*(1-0.65)/55)

=0.64

It is a two-tailed test.

Given 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=0.64 is between -1.96 and 1.96, we do not reject the null hypothesis.

Answer: Yes, because the test value 0.64 is in the noncritical region.