A test was made of H0: μ1 = μ2 versus H1: μ1 < μ2. The sample means were and the sample standard deviations were and and the sample sizes were and Is H0 rejected at the 0.05 level? (Hint: First compute the value of the test statistic.)

Step-by-step explanation:

Hello!

Hypotheses:

H₀: μ₁ = μ₂

H₁: μ₁ < μ₂  

α: 0.05

Using the following sample information:

Sample 1

n₁= 15

X[bar]₁= 10

S₁= 4

Sample 2

n₂= 27

X[bar]₂= 8

S₂= 7

This is an example of a t-test for independent samples, assuming both unknown populations variances are equal the statistic is:

The p-value of this test is 0.1593

To decide using the p-value approach you have to use the following rule:

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

The calculated p-value is greater than the significance level, the decision is to not reject the null hypothesis.

Using a 5% significance level you can conclude that the hypothesis test is not significant and the population means of populations 1 and 2 are equal.

I hope this helps!

.mp4 files, because, video

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6