3) Determine if the conditions required for the normal approximation to the binomial are met. If so, calculate the test statistic, determine the critical value(s), and use that to decide whether there is sufficient evidence to reject the null hypothesis or not at the given level of significance.

H0 : p=0.85

H1 : p 0.85

p=0.778

n=128

=0.05

a. Calculate the test statistic.

z=

Round to two decimal places if necessary

Enter 0 if normal approximation to the binomial cannot be used

________________________________________

b. Determine the critical value(s) for the hypothesis test.

+

Round to two decimal places if necessary

Enter 0 if normal approximation to the binomial cannot be used

________________________________________

c. Conclude whether to reject the null hypothesis or not based on the test statistic.

Reject

Fail to Reject

4) A random sample ofn1=21securities in Economy A produced mean returns ofx1=5.3%withs1=2.5%while another random sample ofn2=16securities in Economy B produced mean returns ofx2=4.7%withs2=1.9%..At=0.01, can we infer that the returns differ significantly between the two economies?

Assume that the samples are independent and randomly selected from normal populations withequal population variances(1²=2²)

a.Calculate the test statistic.

t=

Round to three decimal places if necessary

b.Determine the critical value(s) for the hypothesis test.

+

Round to three decimal places if necessary

c.Conclude whether to reject the null hypothesis or not based on the test statistic.

Reject

Fail to Reject