Medical tests were conducted to learn about drug-resistant tuberculosis. of 142 cases tested in new jersey, 9 were found to be drug-resistant. of 268 cases tested in texas, 5 were found to be drug-resistant. do these data suggest a statistically significant difference between the proportions of drug-resistant cases in the two states? use a .02 level of significance. what is the p-value, and what is your conclusion?

Step-by-step explanation:

Hello!

Sample 1 (New Jersey)

n₁= 142

x₁= 9

^ρ₁=9/142=0.063

Sample 2 (Texas)

n₂= 268

x₂= 5

^ρ₂= 5/268 = 0.0186 ≅ 0.019

Since what you need to test is if there is a significant difference between the proportions of drug-resistant cases in both states, the hypothesis are:

H₀: ρ₁-ρ₂=0

H₁: ρ₁-ρ₂≠0

α:0.20

The equation of the statistic is:

Z= (^ρ₁-^ρ₂)-(^ρ₁-^ρ₂)

 √(^ρ(1-ρ)(1/n₁+1/n₂))

Where ^ρ= x₁+x₂

                  n₁+n₂

The calculated statistic is Z=2.2804

and the p-value= 0.0226

Since the p-value is less than the level of signification, you can reject the null hypothesis. This means that there is enough evidence to conclude that there is a significant difference between the proportion of drug-resistant tuberculosis in both states.

  5.   y=6; de=7; fg=8

  6.   x=4.2; jl=14.2; mn=13

step-by-step explanation:

when chords cross inside a circle, the product of the segment lengths is a constant.

5. dh×eh = fh×gh

  y = gh = dh×eh/fh = 3×4/2 . . . divide by the coefficient of gh

  y = 6

of course, the total chord length is the sum of the lengths of its segments.

  de = dh +eh = 3+4 = 7

  fg = fh +gh = 2+6 = 8

6. this problem works the same way as the previous one.

  x = lk = mk×nk/jk = 6×7/10 = 4.2

  jl = jk +lk = 10 +4.2 = 14.2

  mn = mk +nk = 6 +7 = 13

comment on chords and secants

you can think of the points h (problem 5) and k (problem 6) as points where the chords meet. a chord is part of a secant line, a line that intersects the circle in two points. one can also consider these points (h or k) to be the points where the respective secant lines meet.

then, the product that is a constant is the product of the distance from the meeting point (h or k) to one circle intersection with the distance from that meeting point to the other circle intersection. for problem 5, the constant is the product hd×he = hf×hg.

it turns out that this rule regarding the products of lengths to points of intersection is also true when the secants intersect outside the circle.

that is, you only need to remember one rule to work both kinds of problems.

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step-by-step explanation: