A sprinkler system is being installed in a newly renovated building on campus. The average activation time is supposed to be at most 20 seconds. A series of 12 fire alarm/sprinkler system tests results in an average activation time of 21.5 seconds. Do these data indicate that the design specifications have not been met? The hypotheses to be tested are H0: m = 20 versus Ha: m > 20, where m = the true average activation time of the sprinkler system. Assume that activation times for this system are Normally distributed with s = 3 seconds. (a) What is the value of the observed test statistic?
(b) What is the value of the P-value?
(c) Are the data statistically significant at the 5% significance level? Explain briefly.
(d) What does the decision you made mean with respect to the question "Do these data indicate that the design specifications have not been met?"
(e) If the true average activation time of the sprinkler system is, in fact, equal to 20 seconds, what type of error would you have made?

What is an equation of the line that passes through the point (-2,3) and is parallel to the line whose equations is y=3/2x-4? i am stuck between y=3/2x or y=3/2x+6 : (

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.

For the inequality |c| < |d| to be true, which of the following must be true?