In a study of cell phone usage and brain hemispheric dominance, an Internet survey was e-mailed to 6997 subjects randomly selected from an online group involved with ears. There were 12961296 surveys returned. Use a 0.01 significance level to test the claim that the return rate is less than 20%. Use the P-value method and use the normal distribution as an approximation to the binomial distribution.

Since the p value is very low we have enough evidence to reject the null hypothesis at the significance lvel given of 0.01 so then we can conclude that the return rate ofr this case is significantly lower than 20%

Step-by-step explanation:

Data given

n=6997 represent the random sample taken

X=1296 represent the returned surveys

estimated proportion of  returned surveys

is the value that we want to test

z would represent the statistic (variable of interest)

represent the p value (variable of interest)  

System of hypothesis

We need to conduct a hypothesis in order to test the claim that the true proportion of returned surveys is less than 0.2.:  

Null hypothesis:  

Alternative hypothesis:  

The statistic is given by:

(1)  

Calculate the statistic  

Since we have all the info required we can replace in formula (1) like this:  

Statistical decision  

The next step would be calculate the p value for this test.  

Since is a left tailed test the p value would be:  

Since the p value is very low we have enough evidence to reject the null hypothesis at the significance lvel given of 0.01 so then we can conclude that the return rate ofr this case is significantly lower than 20%

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.