Mathematics, 19.02.2021 16:30 cbrewer37

According to an AP-Ipsos poll (June 15, 2005), 42% of 1001 randomly selected adult Americans made plans in May 2005 based on a weather report that turned out to be wrong. a. Construct and interpret a 99% confidence interval for the proportion of Americans who made plans in May 2005 based on an incorrect weather report.
b. Do you think it is reasonable to generalize this estimate to other months of the year

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a) The 99% confidence interval for the proportion of Americans who made plans in May 2005 based on an incorrect weather report is (0.3798,0.4602). This means that we are 99% sure that the true population proportion is in this interval.

b) No, since May is a month with a wide range of possible weather.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

42% of 1001 randomly selected adult Americans made plans in May 2005 based on a weather report that turned out to be wrong.

This means that p = 0.42, n = 1001

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so Z = 2.575 .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 - 2.575\sqrt{\frac{0.42*0.58}{1001}} = 0.3798$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 + 2.575\sqrt{\frac{0.42*0.58}{1001}} = 0.4602$

The 99% confidence interval for the proportion of Americans who made plans in May 2005 based on an incorrect weather report is (0.3798,0.4602). This means that we are 99% sure that the true population proportion is in this interval.

b. Do you think it is reasonable to generalize this estimate to other months of the year

No, since May is a month with a vast number of possible outcomes, as it is in the spring, not being in the winter(cold) or summer(hot), which means that it can be both hot or cold, wet or dry,...

Answer from: Quest

(- 1, 0 )

step-by-step explanation:

an x- intercept is where the function crosses the x- axis.

to find the x- intercept/s look for the value of x when f(x) = 0

from the given table there are 3 values of x where f(x) = 0

when x = - 1, x = 2, x = 3

the one that is listed is (- 1, 0 )

Which is an x-intercept of the continuous function in the table

Answer from: Quest

step-by-step explanation:

assume that you have 3 different side lengths. apply the pythagorean theorem here: square each of the two shortest sides; call them a and b, so that their squares are a² and b². also square the longest side, calling the result c².

now, if a² + b² = c² is true, the triangle is a right triangle; otherwise it is not a right triangle.

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