Aresearcher wished to compare the effect of two stepping heights (low and high) on heart rate in a step‑aerobics workout. a collection of 50 adult volunteers was randomly divided into two groups of 25 subjects each. group 1 did a standard step‑aerobics workout at the low height. the mean heart rate at the end of the workout for the subjects in group 1 was ¯1=90 beats per minute with a standard deviation of =9 beats per minute. group 2 did the same workout but at the high step height. the mean heart rate at the end of the workout for the subjects in group 2 was ¯2=95.08 beats per minute with a standard deviation of =12 beats per minute. assume that the two groups are independent and that the data are approximately normal. let and represent the mean heart rates we would observe for the entire population represented by the volunteers, if all members of this population did the workout using the low or high step height, respectively. suppose the researcher wished to test the hypotheses : = and : < . using the conservative value for the degrees of freedom, the ‑value for the test is: between 0.1 and 0.05. between 0.05 and 0.01. larger than 0.1.

Evaluate the expression for the given value of the variable 2×(c2-5) for c=4

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.

Solve this equation using substitution. {4x + y = −2} {4x + 6y = 44}