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3 years ago

The endpoints of a diameter of a circle are (4,-2) and (3,6). Find the area of the circle in terms of pi

1 answer:

4 0

The endpoints of a diameter of a circle are (4,-2) and (3,6). The area of the circle in terms of pi is 65pi
First, is to get the length of the diameter by getting the distance of the two points: (4, -2) and (3, 6)

dis = sqrt( (x2-x1)^2 + (y2-y1)^2)
dis = sqrt( (3-4)^2 + (6--2)^2 )
dis = sqrt( 1 + 64 )
dis = sqrt(65)

Next, is to find the area of the circle:
A = pi * r^2
A = pi * (sqrt(65))^2
A = 204.20 square units

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Null and alternative hypothesis

$H_0: \pi \geq0.25\\\\H_1: \pi$

Test statistic $z=-26.82$

P-value $P=0$

The null hypothesis is rejected.

It is concluded that the proportion of households tuned into the program is less than 25%. The claim of the advertiser is rigth and got statistical support.

Step-by-step explanation:

We have to perform a hypothesis test of a proportion.

The claim is that less than 25% were tuned into the program, so we will state this null and alternative hypothesis:

$H_0: \pi \geq0.25\\\\H_1: \pi$

The signifiance level is 0.01.

The sample has a proportion p=0.1 and sample size of n=6000.

The standard deviation of the proportion, needed to calculate the test statistic, is:

$\sigma_p=\sqrt{\frac{\pi(1-\pi)}{N} } =\sqrt{\frac{0.25(1-25)}{6000} } =0.0056$

The test statistic is calculated as:

$z=\frac{p-\pi+0.5/N}{\sigma_p} =\frac{0.1-0.25+0.5/6000}{0.0056}=\frac{-0.1499}{0.0056} =-26.82$

As this is a one-tailed test, the P-value is P(z<-26.82)=0. The P-value is smaller than the significance level (0.01), so the effect is significant.

Since the effect is significant, the null hypothesis is rejected. It is concluded that the proportion of households tuned into the program is less than 25%. The claim of the advertiser is rigth and got statistical support.

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3 years ago