Suppose a recent random sample of employees nationwide that have a 401(k) retirement plan found that 18 of them had borrowed against it in the last year.
A random sample of 100 employees from a local company who have a 401(k) retirement plan found that 14 had borrowed from their plan. Based on the sample results, is it possible to conclude, at the = 0.025 level of significance, that the local company had a lower proportion of borrowers from its 401(k) retirement plan than the 18 reported nationwide?A) The z-critical value for this lower tailed test is z = -1.96. Because -1.5430 is greater than the z-critical value we do not reject the null hypothesis and conclude that the proportion of employees at the local company who borrowed from their 401(k) retirement plan is not less than the national average.
B) The z-critical value for this lower tailed test is z = -1.96. Because -1.0412 is greater than the z-critical value we do not reject the null hypothesis and conclude that the proportion of employees at the local company who borrowed from their 401(k) retirement plan is not less than the national average.
C) The z-critical value for this lower tailed test is z = 1.96. Because 1.5430 is less than the z-critical value we do not reject the null hypothesis and conclude that the proportion of employees at the local company who borrowed from their 401(k) retirement plan is not less than the national average.
D) The z-critical value for this lower tailed test is z = 1.96. Because 1.0412 is less than the z-critical value we do not reject the null hypothesis and conclude that the proportion of employees at the local company who borrowed from their 401(k) retirement plan is not less than the national average.
Question 2
The manager for State Bank and Trust has recently examined the credit card account balances for the customers of her bank and found that 20 have an outstanding balance at the credit card limit.
Suppose the manager randomly selects 15 customers and finds 4 that have balances at the limit. Assume that the properties of the binomial distribution apply.What is the probability of finding 4 customers in a sample of 15 who have maxed out their credit cards?A) 0.1876
B) 0.8358
C) 0.6482
D) 0.3832
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