Question

In: Statistics and Probability

Sparr Investments, Inc., specializes in tax-deferred investment opportunities for its clients. Recently Sparr offered a payroll...

Sparr Investments, Inc., specializes in tax-deferred investment opportunities for its clients. Recently Sparr offered a payroll deduction investment program for the employees of a particular company. Sparr estimates that the employees are currently averaging $100 or less per month in tax-deferred investments. A sample of 35 employees will be used to test Sparr's hypothesis about the current level of investment activity among the population of employees. Assume the employee monthly tax-deferred investment amounts have a population standard deviation of $75 and that a 0.05 level of significance will be used in the hypothesis test.

(a)

What is the probability of the type II error if the actual mean employee monthly investment is $125? (Round your answer to four decimal places. If it is not possible to commit a type II error enter NOT POSSIBLE.)

(b)

What is the probability of the type II error if the actual mean employee monthly investment is $130? (Round your answer to four decimal places. If it is not possible to commit a type II error enter NOT POSSIBLE.

(c)

Assume a sample size of 70 employees is used and repeat parts (b) and (c).

What is the probability of the type II error if the actual mean employee monthly investment is $125? (Round your answer to four decimal places. If it is not possible to commit a type II error enter NOT POSSIBLE.)

What is the probability of the type II error if the actual mean employee monthly investment is $130? (Round your answer to four decimal places. If it is not possible to commit a type II error enter NOT POSSIBLE.)

Solutions

Expert Solution

(a)

3 steps...

(i) Find the critical value - the value that separates the rejection region from fail to reject region.

= Ho value + z * sigma/sqrt(n)
= 100 + 1.645 * 75 / sqrt(35)
= 120.8542

(ii) Find the z-score for the xbar critical value using the true value for mu

z = (-)/(/sqrt(n))
z = (120.8542-125)/(75/sqrt(35))
z = -0.327

(iii) Find the probability that z < -0.327 (since we are testing greater than)

beta = P(xbar crit < 120.8542 given = 125)
beta = P(z < -0.327)
beta = 0.0005

the probability of the type II error if the actual mean employee monthly investment is $125 is 0.0005

(b)

xbar = 100 + 1.645 * 75 / sqrt(35) = 120.8542
z = (120.8542-130)/(75/sqrt(35)) = -0.7214
beta = 0.2358

the probability of the type II error if the actual mean employee monthly investment is $130 is 0.2358

(c)

* When mu = 125 and n = 70

= 100 + 1.645 * 75 / sqrt(70) = 113.763

z = (113.763-125)/(75/sqrt(70)) = -1.343

beta = 0.3669

* When mu = 130 and n = 70

= 100 + 1.645 * 75 / sqrt(70) = 113.79

z = (113.763-130)/(75/sqrt(70)) = -1.94

beta = 0.0262

orchestra answered 2 years ago
Next > < Previous

Related Solutions

Eric Roberts, Inc. is a company that specializes in tax-deferred investment opportunities for its clients. Recently,...
Eric Roberts, Inc. is a company that specializes in tax-deferred investment opportunities for its clients. Recently, this company offered a payroll deduction investment program for the employees of a particular company. The company estimates that the employees are currently averaging $110 or less per month in tax-deferred investments. A sample of 80 employees will be used to test the company’s hypothesis about the current level of investment activity among the population of employees. Assume the employee monthly tax-deferred investment amounts...
Blair & Rosen, Inc. (B&R) is a brokerage firm that specializes in investment portfolios designed to meet the specific risk tolerances of its clients
  Blair & Rosen, Inc. (B&R) is a brokerage firm that specializes in investment portfolios designed to meet the specific risk tolerances of its clients. A client who contacted B&R this past week has a maximum of $50,000 to invest. B&R's investment advisor decides to recommend a portfolio consisting of two investment funds: an Internet fund and a Blue Chip fund. The Internet fund has a projected annual return of 12%, while the Blue Chip fund has a projected annual...
Dottie’s Tax Service specializes in tax returns for professional clients, such as physicians, dentists, accountants, and...
Dottie’s Tax Service specializes in tax returns for professional clients, such as physicians, dentists, accountants, and lawyers. A recent audit of the returns she prepared indicated that an error was made on 4.2 percent of the returns she prepared last year.    Use the normal approximation to the binomial distribution to answer all parts of this question. Assuming this rate continues into this year and she prepares 44 returns, what is the probability that she makes errors on a. More than...
Dottie's Tax Service specializes in federal tax returns for professional clients, such as physicians, dentists, accountants,...
Dottie's Tax Service specializes in federal tax returns for professional clients, such as physicians, dentists, accountants, and lawyers. A recent audit by the IRS of the returns she prepared indicated that an error was made on 15% of the returns she prepared last year. Assuming this rate continues into this year and she prepares 52 returns, what is the probability that she makes errors on: More than 8 returns? (Round your z-score computation to 2 decimal places and final answer...
Dottie's Tax Service specializes in federal tax returns for professional clients, such as physicians, dentists, accountants,...
Dottie's Tax Service specializes in federal tax returns for professional clients, such as physicians, dentists, accountants, and lawyers. A recent audit by the IRS of the returns she prepared indicated that an error was made on 11% of the returns she prepared last year. Assuming this rate continues into this year and she prepares 67 returns, what is the probability that she makes errors on: a. More than 7 returns? (Round z-score computation to 2 decimal places and your final...
Dottie's Tax Service specializes in federal tax returns for professional clients, such as physicians, dentists, accountants,...
Dottie's Tax Service specializes in federal tax returns for professional clients, such as physicians, dentists, accountants, and lawyers. A recent audit by the IRS of the returns she prepared indicated that an error was made on 10% of the returns she prepared last year. Assuming this rate continues into this year and she prepares 62 returns, what is the probability that she makes errors on: a) More than 6 returns? b) At least 6 returns? c) Exactly 6 returns?
Suppose an investor, Erik, is offered the investment opportunities described in the table below. Each investment...
Suppose an investor, Erik, is offered the investment opportunities described in the table below. Each investment costs $1,000 today and provides a payoff, also described below, one year from now. Option Payoff One Year from Now 1 100% chance of receiving $1,100 2 50% chance of receiving $1,000 50% chance of receiving $1,200 3 50% chance of receiving $200 50% chance of receiving $2,000 If Erik is risk averse, which investment will he prefer? The investor will choose option 1....
Transcendental Advisors is advising one of their corporate clients on potential investment opportunities. The advisors are...
Transcendental Advisors is advising one of their corporate clients on potential investment opportunities. The advisors are presented with two business strategies (a and b below). The company expects the profit to be $2,000,000 a year with no growth. The company also operates tax-exempt and is subject to 8.6% p.a. cost of capital compounded annually. The company long-term borrowing rate is 5.9% p.a. compounded annually. a) Spend $5,000,000 to expand existing operations, boosting current expected annual profit from $2,000,000 to $3,000,000....
If employees are averaging $120 or less per month in tax-deferred investments. A sample of 80...
If employees are averaging $120 or less per month in tax-deferred investments. A sample of 80 employees will be used to test the hypothesis about the current level of investment activity among the population of employees. Assume the employee monthly investment has a std deviation of $75 and a 0.01 level of significance. what is the probability of the type II error? what is the probability if the monthly investment mean is $140?
Illusions Inc. just completed its second year of operations and has a deferred tax asset of?...
Illusions Inc. just completed its second year of operations and has a deferred tax asset of? $47,500 related to a net operating loss of? $125,000 from the previous year. In the current year Illusions generates? $400,000 in revenues and incurs? $250,000 in expenses. There are no permanent or temporary? book-tax differences. Assuming the same tax rate as last? year, what amount will Illusions record for Income Tax Payable in the current? year?
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT