A random sample of 150 donations at a certain blood bank reveals that 70 were Type A blood. Does this suggest that the actual percentage of Type A donations differs from 40%, the percentage of the population having Type A blood? Carry out a test of hypotheses using a significance level of 0.01. Would your conclusion have been different if significance level of 0.05 had been used? Use only the P-Value Approach. State H0 and Ha. (20 pts)

Now we can calculate th p value using the alternative hypothesis with the following probability:

Since the p value is higher than the significance level given of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion of Type A donations  is not significantly different from 0.4 or 40% at 5% of significance.

Step-by-step explanation:

Information given

n=150 represent the random sample taken

X=70 represent the samples with Type A blood

estimated proportion of samples with Type A blood

is the value to verify

represent the significance level

zwould represent the statistic

represent the p value

System of hypothesis

We want to verify if the actual percentage of Type A donations differs from 40%, then the system of hypothesis are:  

Null hypothesis:  

Alternative hypothesis:  

The statistic is given by:

(1)  

Replacing the info given we got:

Now we can calculate th p value using the alternative hypothesis with the following probability:

Since the p value is higher than the significance level given of 0.05 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion of Type A donations  is not significantly different from 0.4 or 40% at 5% of significance.

2160ft3

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240