Suppose that, in 1995, the weight of 16-year old males in the united states was normally distributed with a mean of 143 lbs and standard deviation equal to 15 lbs. suppose that roger, a public health researcher, believes that the popularity of video and computer gaming has made teenagers less active, and predicts that 16-year old males today weigh more than 16-year old males did in 1995. to test the theory, he chooses a random sample of 50 16-year old males and records their weights. the average weight of the sample is 147 lbs. roger uses a z ‑ test to test the hypothesis that the average weight of 16-year old males has increased. he calculates the z ‑ statistic as 1.89 standard deviations above the mean. use this standard normal z-distribution table to calculate the p-value of this statistic. give your answer as a decimal rounded to four places. also how to determin if this is a one-sided or two-sided test?

Step-by-step explanation:

The null hypothesis is:

H0: μ(1995)=μ(2019)

The alternative hypothesis is:

H1: μ(1995)<μ(2019)

Because Roger wants to know if mean weight of 16-old males in 2019 is more than the mean weight of 16-old males in 1995 the test only uses one tail of the z-distribution.  It is not a  two-sided test because in that case the alternative hypothesis would be:  μ(1995)≠μ(2019).

To know the p-value, we use the z-statistic, in this case 1.89 and the significance level. Because the problem does not specify it, we will search for the p-value at a 5% significance level and at a 1%.

For a z of 1.89 and 5% significance level, the p-value is: 0.9744

For a z of 1.89 and 1% significance level, the p-value is: 0.9719

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2