Asurvey of 100 similar-sized hospitals revealed a mean daily census in the pediatrics service of 27 with a standard deviation of 6.5. researchers test whether these data provide sufficient evidence to indicate the mean is greater than 25. use α=.05. give 1. the hypotheses, 2. appropriate test, 3. decision rule, 4. calculated test statistic, and 5. conclusion with a comparison to the critical value or alpha.

We conclude that the mean is greater than 25.  

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 25

Sample mean, = 27

Sample size, n = 100

Alpha, α = 0.05

Sample standard deviation, s = 6.5

First, we design the null and the alternate hypothesis

We use One-tailed(right) z test to perform this hypothesis.

Formula:

Putting all the values, we have

Now,

Since,  

We reject the null hypothesis and accept the alternate hypothesis.

Thus,  the mean is greater than 25.

cut 138 centimeters off

step-by-step explanation:

250-112 = 138

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 .