1.
If it is appropriate to do so, use the normal approximation to the p̂-distribution to calculate the indicated probability:
n=80,p=0.715
P( p̂ > 0.75)=
Enter 0 if it is not appropriate to do so.
2.
A manager at a local discount gym believes that less than 20% of gym members use the gym, at least 5 days a week. She randomly selects 100 gym members and tracks (using the electronic login system at the door) how many days they used the gym over the 2-week period. The following are the results:
2, 3, 10, 4, 2, 3, 8, 4, 8, 10, 5, 0, 6, 3, 9, 13, 6, 3, 12, 5, 3, 3, 5, 1, 5, 9, 8, 5, 8, 2, 6, 4, 4, 2, 12, 1, 3, 3, 2, 12, 7, 3, 14, 2, 8, 5, 2, 6, 1, 5, 6, 9, 6, 8, 10, 1, 11, 3, 2, 1, 5, 4, 1, 2, 3, 13, 7, 4, 8, 3, 7, 4, 3, 2, 10, 3, 1, 7, 11, 8, 4, 7, 6, 7, 8, 11, 7, 6, 3, 2, 5, 0, 4, 6, 5, 12, 2, 10, 1, 2
Test the manager's claim at the 2.5% level of significance.
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
Cannot Use Normal Approximation to Binomial
3.
A random sample of n1=19 securities in Economy A produced mean returns of x̄1=5.9% with s1=2% while another random sample of n2=18 securities in Economy B produced mean returns of x̄2=4.6% with s2=2.2%. At α=0.1, can we infer that the returns differ significantly between the two economies?
Assume that the samples are independent and randomly selected from normal populations with equal population variances (σ1²=σ2²)
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