Assume that you have a sample of n1=9, with the sample mean X1=46, and a sample standard deviation of S1=4, and you have an independent sample of n2=12 from another population with a sample mean of X2=31 and the sample standard deviation S2=5. Complete parts (a) through (d) below. a. What is the value of the pooled-variance tSTAT test statistic for testing H0: μ1=μ2? tSTAT=nothing (Round to two decimal places as needed.) b. In finding the critical value, how many degrees of freedom are there? nothing degrees of freedom (Simplify your answer.) c. Using a significance level of α=0.1, what is the critical value for a one-tail test of the hypothesis H0: μ1≤ μ2 against the alternative H1: μ1>μ2? The critical value is nothing. (Round to two decimal places as needed.) d. What is your statistical decision? A. Reject H0 because the computed tSTAT test statistic is greater than the upper-tail critical value. B. Reject H0 because the computed tSTAT test statistic is less than the upper-tail critical value. C. Do not reject H0 because the computed tSTAT test statistic is less than the upper-tail critical value. D. Do not reject H0 because the computed tSTAT test statistic is greater than the upper-tail critical value.

a. t`= 7.63

b.υ = [s₁²/n1 + s₂²/n2]²/ (s₁²/n1 )²/ n1-1 + (s₂²/n2)²/n2-1

= 18.885 ≈19 The degrees of freedom is always rounded in this calculation.

c. The critical region for one tailed test for alpha= 0.1 and 19 degrees of freedom is 1.328= 1.33

The critical region is ║t║` ≥ t 0.05,19 = 1.729= 1.73

A. Reject H0 because the computed tSTAT test statistic is greater than the upper-tail critical value

Step-by-step explanation:

Step-by-step explanation:

We state our null and alternative hypothesis as

H0: μ1=μ2 against Ha: μ1 ≠ μ2

The level of significance is α=0.1

Since the population have unequal variances , the test statistic if H0 is true ,is

t`= x1`- x2`/ √s₁²/n1 + s₂²/n2

which has approximately a t- distribution with υ degrees of freedom where

υ = [s₁²/n1 + s₂²/n2]²/ (s₁²/n1 )²/ n1-1 + (s₂²/n2)²/n2-1

Computations:

t`= x1`- x2`/ √s₁²/n1 + s₂²/n2

t`= 46-31/ √4²/9 + 5²/12

t`= 15/√16/9 +25/12

t`= 15/ √64+75/36

t`=15/1.9649

t`=7.6339

t`= 7.63

υ = [s₁²/n1 + s₂²/n2]²/ (s₁²/n1 )²/ n1-1 + (s₂²/n2)²/n2-1

= [139/36]²/ (16/9)²/8 +(25/12)²/11

= 14.91/ 0.395 + 0.395

= 18.885

≈19 The degrees of freedom is always rounded in this calculation.

The critical region is ║t`║≥ t 0.05,19 = 1.729

Since the calculated value of t` falls in the critical region we reject our null hypothesis of equal means.

this is answer of 144 cubic meters