From a random sample of 50 people, sitting pulse rates and standing pulse rates were measured for each person. A coin was flipped to determine whether the sitting or the standing pulse rate would be measured first. Let μsitting represent the mean sitting pulse rate in the population, μstanding represent the mean standing pulse rate of the population, and μd represent the mean difference between the sitting and standing (sitting – standing) pulse rates of the population. Which of the following represents an appropriate test and hypotheses to determine if there is a difference in mean pulse rates between sitting and standing in the population?1. A two-sample t-test withH0 : μsitting = μstandingHA : μsitting ≠ μstanding2. A two-sample t-test withH0 : μsitting = μstandingHA : μsitting < μstanding3. A matched-pairs t-test withH0 : μd = 0HA : μd ≠ 04. A matched-pairs t-test withH0 : μd = 0HA : μd < 0

3. A matched-pairs t-test with H0 : μd = 0,  HA : μd ≠ 0

Step-by-step explanation:

An investigator wants to asses the difference in mean pulses rates between sitting and standing persons in population.

The matched paired t-test is appropriate choice because the observations in the data are paired. The observations in the data are the calculated pulse rates of 50 persons while sitting and standing. For each person. sitting and standing pulse rates are measured and this indicates the before and after effect is measured. The before and after effect is measured through matched paired t test.

Also,  an investigator wants to determine whether there is difference in mean pulse rates between sitting and standing in population. This indicates two tailed test. so, the hypotheses would be

Null hypotheses : μd = 0

Alternative hypotheses: μd ≠ 0.

Thus, situation indicates a matched-pairs t-test with H0 : μd = 0,  HA : μd ≠ 0.

99

step-by-step explanation:

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.