Question

Hypothesis tests for the three comparisons (1 and 2, 1 and 3, and 2 and 3) Use a 2-tail test

Create own scenario and perform the test?

4.5 165 Screenshot attached below Age Height Weight in lbs 4.2 120 5.4 140 6.3 132 4.9 131 210 11 5.3 5.8 189 5.1 6.1 5.11 4.2 166 125 178 120 37.533 5.247333333 142.4666667 Mean 27.318 0.762256675 45.51430963 Standard Deviation! 174 132 5.7

Answer 1

Solution:Using Minitab

a)MTB > TwoT 15 37.533 27.318 15 5.248 0.7622;
SUBC> Confidence 95.0;
SUBC> Test 0.0;
SUBC> Alternative 0.

Two-Sample T-Test and CI

Sample N Mean StDev SE Mean
1 15 37.5 27.3 7.1
2 15 5.248 0.762 0.20

Difference = μ (1) - μ (2)
Estimate for difference: 32.29
95% CI for difference: (17.15, 47.42)
T-Test of difference = 0 (vs ≠): T-Value = 4.58 P-Value = 0.000 DF = 14

b)MTB > TwoT 15 37.533 27.318 15 142.47 45.514;
SUBC> Confidence 95.0;
SUBC> Test 0.0;
SUBC> Alternative 0.

Two-Sample T-Test and CI

Sample N Mean StDev SE Mean
1 15 37.5 27.3 7.1
2 15 142.5 45.5 12

Difference = μ (1) - μ (2)
Estimate for difference: -104.9
95% CI for difference: (-133.4, -76.5)
T-Test of difference = 0 (vs ≠): T-Value = -7.66 P-Value = 0.000 DF = 22

c)MTB > TwoT 15 5.2473 0.7622 15 142.47 45.514;
SUBC> Confidence 95.0;
SUBC> Test 0.0;
SUBC> Alternative 0.

Two-Sample T-Test and CI

Sample N Mean StDev SE Mean
1 15 5.247 0.762 0.20
2 15 142.5 45.5 12

Difference = μ (1) - μ (2)
Estimate for difference: -137.2
95% CI for difference: (-162.4, -112.0)
T-Test of difference = 0 (vs ≠): T-Value = -11.68 P-Value = 0.000 DF = 14

Using Excel:

F K L t-Test: Two-Sample Assuming Unequal Variances Age Height Weights Age-Height 4.2 5.4 Age Height 37.5333333 5.24733333 746.266667 0.58103524 6.3 Mean Variance Observations Hypothesized Mean Difference 4.9 15 df 5.3 5.8 5.1 6.1 5.11 120 140 132 131 210 11 165 189 174 132 144 166 125 178 t Stat PIT<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 14 4.57555571 0.00021606 1.76131014 0.00043212 2.14478669 p-val 4.2 5.7 t-Test: Two-Sample Assuming Unequal Variances 120 Age-Weight t-Test: Two-Sample Assuming Unequal Variances Age Weights 37.5333333 142.466667 746.266667 2071.55238 15 15 21 Height-Weight Height Weights 5.24733333 142.466667 0.58103524 2071.55238 Mean Variance Observations Hypothesized Mean Difference df t Stat P(T<=t) one-tail t Critical one-tail PIT<=t) two-tail t Critical two-tail 0 23 15 15 Mean Variance Observations Hypothesized Mean Difference df t Stat P(TC=t) one-tail t Critical one-tail p-val P(T<=t) two-tail t Critical two-tail O -7.656011 4.5203E-08 1.71387153 9.0406E-08 2.06865761 p-val 14 -11.6748706 6.6483E-09 1.76131014 1.3297E-08 2.14478669

Conclusion:

from above all test P-value << $\alpha$ .

We Reject all the hypothesis.