The average birthweight for babies in the United States is 3,325 grams with σ = 525. A researcher wishes to test whether or not a sample of 250 women in a rural community have a significantly different average birthweight than the national average at the α = 0.05 level. The mean birthweight for the sample of women in the rural community is 3400 grams.

a) what is the degree of freedom in this study?

b)what is the test statistic?

c) is the finding statistically significant?

The test statistic is z =

the z- value is 2.25 > 1.96 at 5% level of significance

we will not accepted null hypothesis

the mean (x⁻) and μ do not differ significantly

Step-by-step explanation:

Step 1:-

Given n = 250 and

population mean(μ ) = 3325 and

standard deviation of population (σ )= 525

mean of the sample ( x ) = 3400

i) Null hypothesis (H0) : (μ ) = 3325

ii) alternative hypothesis(H1) :(μ )≠ 3325

iii) The level of significance ∝ =0.05 = 1.96

Step 2 :-

The test statistic z =

now substitute all these values , we get

on simplification

  z = 2.25

The tabulated value z = 1.96 at 5% level of significance (from z- table)

The calculated value  z = 2.25 > tabulated value 1.96 at 0.05 level of significance

There fore the null hypothesis is rejected at 5% level of significance.

Therefore is not statistically significant

conclusion:-

The null hypothesis is rejected at 5% level of significance.

Therefore that is not statistically significant

(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