An article in the Journal of Materials Engineering (Vol 11, No. 4, 1989, pp. 275-282) reported the results of an experiment to determine failure mechanisms for plasma-sprayed thermal barrier coatings. The failure stress for one particular coating (NiCrAlZr) under two different test conditions is as follows:
Failure stress ( times 10^6 Pa) after nine 1-hr cycles: 19.8, 18.5, 17.6,16.7, 16.7, 14.8, 15.4, 14.1, 13.6
Failure stress ( times 10^6 Pa) after six 1-hr cycles: 14.9, 12.7, 11.9, 11.4, 10.1,7.9
(a) What assumptions are needed to construct confidence intervals for the difference in mean failure stress under the two different test conditions? Use normal probability plots of the data to check these assumptions.
(b) Perform a hypothesis test to determine if the mean failure stress of the two different test conditions is the same at the 0.05 significance level.
(c) Confirm that the P-value of this test is 0.001.

In a sample of 2023 u.s. adults, 373 said franklin roosevelt was the best president since world war ii. two u.s. adults are selected at random from the population of all u.s. adults without replacement. assuming the sample is representative of all u.s. adults, complete parts (a) through (d). (a) find the probability that both adults say franklin roosevelt was the best president since world war ii. the probability that both adults say franklin roosevelt was the best president since world war ii is (round to three decimal places as needed.) (b) find the probability that neither adult says franklin roosevelt was the best president since world war ii. the probability that neither adult says franklin roosevelt was the best president since world war ii is (round to three decimal places as needed.) (c) find the probability that at least one of the two adults says franklin roosevelt was the best president since world war ii. the probability that at least one of the two adults says franklin roosevelt was the best president since world war ii is (round to three decimal places as needed.) (d) which of the events can be considered unusual? explain. select all that apply. the event in part left parenthesis a right parenthesis is unusual because its probability is less than or equal to 0.05. the event in part (b) is unusual because its probability is less than or equal to 0.05. none of these events are unusual. the event in part (c) is unusual because its probability is less than or equal to 0.05.

The length of a rectangle is x times the square root of 100. the width is one-half y more than three-halves x. given that the area of the rectangle is 125 cm2, which equation could represent the rectangle in terms of x and y? a) 5xy − 15x = 125 b) 5xy + 15x = 125 c) 15x2 − 5xy = 125 d) 15x2 + 5xy = 125

The bottom of a slide at the playground is 6 feet from the base of the play set. the length of the slide is 10 feet. how tall is the slide. 11.66 feet 10 feet 6 feet 8 feet