You conduct a simulation regarding which team spectators at a football game support. Your null hypothesis is that there are equal proportions of people supporting the home team and the visiting team. Your alternative hypothesis is that there is a higher proportion of people supporting the home team. You determine that the results of your simulation have a p-value of 0.002. What does this mean?

As the p-value is too small the null hypothesis will be rejected concluding that there is a higher proportion of people supporting the home team.

Step-by-step explanation:

The hypothesis to determine which team spectators at a football game support is:

H₀: There are equal proportions of people supporting the home team and the visiting team, i.e. p₁ = p₂.

Hₐ: There is a higher proportion of people supporting the home team than the visiting team, i.e. p₁ > p₂.

A z-test for difference between proportions can be used to perform the test.

The test statistic is:

Th decision rule is:

If the p-value of the test is less than the significance level α then the null hypothesis will be rejected and vice-versa.

The commonly used significance levels are 0.01, 0.05 and 0.10.

The p-value of the test is computed as, p = 0.002.

The p-value of the test is less than all the significance level.

Thus, the null hypothesis will be rejected at any of the three significance level.

Conclusion:

As the p-value is too small the null hypothesis will be rejected concluding that there is a higher proportion of people supporting the home team.

x = 12

y = 15

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.