Sony would like to test the hypothesis that the average age of a playstation user is different from the average age of an xbox user. a random sample of 36 playstation users had an average age of 34.2 years while a random sample of 30 xbox users had an average age of 32.7 years. assume that the population standard deviation for the age of playstation and xbox users is 3.9 and 4.0 years, respectively. sony would like to set α = 0.10. which one of the following statements is true?

(a) because the p-value is less than α, we reject the null hypothesis and can conclude that the average age of playstation users is different from the average age of xbox users.
(b) because the p-value is less than α, we fail to reject the null hypothesis and conclude that the average age of playstation users is equal to the average age of xbox users.
(c) because the p-value is greater than α, we fail to reject the null hypothesis and cannot conclude that the average age of playstation users is different from the average age of xbox users.
(d) because the p-value is greater than α, we fail to reject the null hypothesis and can conclude that the average age of playstation users is different from the average age of xbox users.

(C) Because the p-value is greater than α, we fail to reject the null hypothesis and cannot conclude that the average age of PlayStation users is different from the average age of Xbox users.

Step-by-step explanation:

The t-statistic for difference of mean is given by,

Using this formula, we get, t = 1.5342

Thus, p-value = 0.1322 with 64 degree of freedom.

and α = 0.10

Since, the p-value is greater than alpha (p > .05), then we fail to reject the null hypothesis, and we say  that the result is statistically non-significant.

look at the picture.

y-intercept for the function on a picture is 4 → point (0, 4).

y-intercept for the function

is for x = 0. substitute:

y-intercept is 8 → point (0, 8).

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough