Statistics and Probability Answers

For which situation Poisson distribution is appropriate to calculate probability of a random event.

The manager of a fleet automobiles is testing two brands of radial tires and assigns

one tire of each brand at random to the two rear wheels of eight cars and runs the

cars until the tires wear out. The data (in kilometers) follow.

Car Brand 1 Brand 2

1 36,925 34,318

2 45,300 42,280

3 36,240 35,500

4 32,100 31,950

5 37,210 38,015

6 48,360 47,800

7 38,200 37,810

8 33,500 33,215

Do the data suggest that the two brands of radial tires prove the same mean life? Use

α = 0.01. [taken from Montgomery, p. 354]

Two companies manufacture a rubber material intended for use in an automotive

application. The part will be subjected to abrasive wear in the field application, so we

decide to compare the material produced by each company in a test. Twenty-five samples of material from each company are tested in an abrasion test, and the amount

of wear after 1000 cycles is observed. For company 1, the sample mean and standard

deviation of wear are x̅1 = 20 milligrams/1000 cycles and s1 = 2 milligrams/1000

cycles, while for company 2 we obtain x̅2 = 15 milligrams/1000 cycles and s2 = 8

milligrams/1000 cycles. [taken from Montgomery, p. 348]

(a) Do the data support the claim that the two companies produce material with

different mean wear? Use α = 0.05, and assume each population is normally

distributed but that their variances are not equal.

(b)What is the P-value for this test?

(c) Do the data support a claim that the material from company 1 has a higher mean

wear than the material from company 2?

Cloud seeding has been studied for many decades as a weather modification

procedure. The rainfall in acre-feet from 20 clouds follows:

18.0 30.7 19.8 27.1 22.3 18.8 31.8 23.4 21.2 27.9

31.9 27.1 25.0 24.7 26.9 21.8 29.2 34.8 26.7 31.6

Can you support the claim that mean rainfall from seeded clouds exceeds 25 acre-

feet? Use α = 0.01. Assume that rainfall is normally distributed. [taken from

Montgomery, p. 306]

An engineer who is studying the tensile strength of a steel alloy intended for use in

golf club shafts knows that tensile strength is approximately normally distributed

with σ = 60 psi. A random sample of 12 specimens has a mean tensile strength of x̅=

3250 psi. (a) Test the hypothesis that mean strength is 3500 psi. use α = 0.01. (b)

What is the smallest level of significance at which you would be willing to reject the

null hypothesis? [taken from Montgomery, p. 300]

I. Read and analyze the given problem. Follow the steps in testing the hypothesis in order to decide whether to reject or fail to reject the null hypothesis.

The owner of the factory that sells a particular bottled fruit juice claimed that the average capacity of their product is 250 ml. To test the claim, a consumer group gets a sample of 100 such bottles, calculates the capacity of cach bottle, and then finds the mean capacity to be 248 ml. The standard deviation s is 5 ml. Use a = 0.05. Will you reject or not to reject the claim.

Step 1: State the hypotheses and identify the claim.

Step 2: Level of significance. Step 3: Find the critical value.

Step 4: Compute the test value.

Step 5: Decision Rule. Step 6: Conclusion..