A random sample of 100 people was taken. Eighty-five of the people in the sample favored Candidate A. At significance level 0.05, we are interested in performing a hypothesis test to determine whether or not the proportion of the population in favor of Candidate A is significantly more than 80%.The critical value is?

We conclude that the proportion of the population in favor of Candidate A is less than or equal to 80%.

Step-by-step explanation:

We are given that a random sample of 100 people was taken. Eighty-five of the people in the sample favored Candidate A.

We are interested in performing a hypothesis test to determine whether or not the proportion of the population in favor of Candidate A is significantly more than 80%.

Let p = proportion of the population in favor of Candidate A

SO, Null Hypothesis, : p 80%   {means that the proportion of the population in favor of Candidate A is less than or equal to 80%}

Alternate Hypothesis, : p > 80%   {means that the proportion of the population in favor of Candidate A is significantly more than 80%}

The test statistics that will be used here is One-sample z proportion statistics;

                                   T.S.  =  ~ N(0,1)

where,  = sample proportion of people favored Candidate A = = 85%

            n = sample of people = 100

So, test statistics  =  

                               =  1.40

Now at 0.05 significance level, the z table gives critical value of 1.6449 for right-tailed test. Since our test statistics is less than the critical value of z so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the proportion of the population in favor of Candidate A is less than or equal to 80%.

Area of the triangle =
We solve for half of one side
half-side^2 = 18.4^2  -17^2
half-side^2 = 338.56 -289
half-side^2 = 49.56
half-side = 7.0398863627
area of polygon = 17 * 7.0398863627 * 8 =
957.4245453298
(This matches the double-check below).


Double-Check
n = number of sides
polygon area = apothem^2 * n * tan (180/n)
polygon area = 17*17 * 8 * tan (22.5)
polygon area = 17*17 * 8 * 0.41421
polygon area = 957.65352

Source:
http://www.1728.org/polygon.htm