Acertain pen has been designed so that true mean writing lifetime under controlled conditions (involving the use of a writing machine) is at least 10 hours. a random sample of 18 pens is selected, the writing lifetime of each is determined, and a normal quantile plot of the resulting data supports the use of a one-sample t test. (a) what hypotheses should be tested if the investigators believe a priori that the design specification has been satisfied? (b) what conclusion is appropriate if the hypotheses of part (a) are tested, t = - 2.3, and α = .05? (c) what conclusion is appropriate if the hypotheses of part (a) are tested, t = - 1.8, and α = .01? (d) what should be concluded if the hypotheses of part (a) are tested and t = - 3.6?

Lois and clark own a company that sells wagons. the amount they pay each of their sales employees (in dollars) is given by the expression 12h+30w12h+30w where hh is the number of hours worked and ww is the number of wagons sold.

Enter the missing numbers in the boxes to complete the table of equivalent ratios of lengths to widths. ? 18 8 ? 10 30 12 ?

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.