Question: The sum of the values obtained in a random sample of size n = 5 is to be used to test the null hypothesis that

The sum of the values obtained in a random sample of size n = 5 is to be used to test the null hypothesis that on the average there are more than two accidents per week at a certain intersection (that λ > 2 for this Poisson population) against the alternative hypothesis that on the average the number of accidents is two or less. If the null hypothesis is to be rejected if and only if the sum of the observations is five or less, find
(a) The probabilities of type I errors when λ = 2.2, 2.4, 2.6, 2.8, and 3.0;
(b) The probabilities of type II errors when λ = 2.0, 1.5, 1.0, and 0.5.]
Also, plot the graph of the power function of this test criterion.

Step by Step Solution

★★★★★

3.25 Rating (166 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Reject if x 5 use Table II b 10 ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

583-M-S-H-T (3205).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Oil viscosity values obtained from two engines are given in DS 9.6.6. Use the rank sum test to assess whether there is any evidence that the engines have different effects on the oil viscosity.

It is possible to construct a nonparametric tolerance interval that is based on the extreme values in a random sample of size n from any continuous population. If p is the minimum proportion of the...

The information about in a random sample of size n is also given by Where f (x) is the value of the population density at x, provided that the extremes of the region for which f(x) 0 do not depend...

Unit 3 Practice Problems Set 16 |Also, note that the templates for hypothesis testing provided in the Excel Guides for this unit are given in the next worksheet 17 lin this document--see folder tabs...

Assume that you are using a significance level of a 5 0.05 to test the claim that p . 0.5 and that your sample is a simple random sample of size n 5 64. a. Assuming that the true population...

Please help me with this thank you 5. Based on a recent census, suppose it is known that the population proportion of Canadians aged 25454 that have a postrsecondary degree is 54%. Interested in...

Lab 10 We will explore 95% confidence interval estimation of a population mean using the t- confidence interval as discussed in Section 11.2 of the text. I. You will be asked to generate 10 random...

Power of a Test Assume that you are using a significance level of a 5 0.05 to test the claim that p , 0.5 and that your sample is a simple random sample of size n 5 1998 with 5 0.48. a. Find b, the...

Let X = {0, 1} and Y be two random variables and let S denote a random sample of size n = 5 from the population. The observations for each individual i in the sample is given by the following table...

What is the best definition of an Operating System? O t is the initial boot up program. It is either Microsoft or Macintosh. The set of commands that help the software programs and hardware interact....

What are the 3 factors that affect the volatility of a diversified portfolio?

When using the Blank 1 method to evaluate capital investments, the company determines the number of years it will take to recover the asset's original Blank 2 though the net Blank 3 generated from...

How will the global economy be different in 2050 compared to today?

Betty and Jane are gambling. They are cutting cards (picking a random place in the deck to see a card). Whichever one has the higher card wins the bet. If the cards have the same value (for example,...

Consider two pairs of grandparents. The first pair has 4 grandchildren and the second pair has 32 grand-children. Which of the two pairs is more likely to have between 40% and 60% boys as...

The graph shows the average when a six-sided die is rolled repeatedly. For example, if the first two rolls resulted in a 6 and a 2, the average would be 4. If the next trial resulted in a 1, the new...

AMT, Inc., is considering the purchase of a digital camera for maintenance of design specifications by feeding digital pictures directly into an engineering workstation where computer-aided design...

You have $ 2 8 8 , 9 8 1 to invest in a stock portfolio ( this amount is your original wealth ) . Your choices are Stock H , with an expected return of 1 5 . 1 percent, and Stock L , with an expected...

Suppose that JPMorgan Chase sells call options on $1.10 million worth of a stock portfolio with beta = 1.45. The option delta is .52. It wishes to hedge out its resultant exposure to a market advance...