Twelve different video games showing violence were observed. The duration times of violence were recorded, with the times (seconds) listed below. What requirements must be satisfied to test the claim that the sample is from a population with a mean greater than 85 sec? Are the requirements all satisfied?

Step-by-step explanation:

Part A :

The requirements (assumption) for testing population mean

1) The Sample are autonomous (not dependent) and normally distributed

2) If the sample size is large ( n >30) then the sampling distribution approaches to normal distribution.

therefore the necessities that are required for testing the claim that the sample is from population with a mean bigger than 80 sec is

D : Either the population is normally distributed or n > 30 or both.

Part B :

To draw normal quantile plot by using R

v <-c(83,13,572,49,0,58,195,41,165,0,2,59)

qqnorm(v)

qqline(v)

From normal qq plot which can be seen from the below attached image, we can see that almost all point on or near the straight line (except one outlier 572).

hence correct answer is

Yes . A normal quantile plot suggests that the sample is from a normally distributed population and there are observation below and above 80.

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.