Question

Conduct an independent samples t-test (a.k.a., between-subjects design). Each sample should have at least n=8 individuals. What to turn in: 1. What is your research question? 2. State the null (Ho) and alternative (H1) hypotheses. 3. Conduct the hypothesis test using an alpha level of .05, and state your conclusion (Reject Ho/Fail to Reject Ho) regarding the original hypotheses. 4. Calculate and interpret a measure of effect size (est. Cohen's d or r2) and a 95% confidence interval.

Answer 1

Independent sample t-test:

Data:

compare wheat and maize grains production per hectare in tons.

wheat	Maize
5.3	6.5
4.5	7.9
6	6.2
6.2	7.6
6.8	5.9
5.8	5.6
5.8	8.2
4.8	6
6.4	7.7
4.8	7
6	5.4
5.1	7.2

1) Research question: compare wheat and maize grains production per hectare in tons.they are equal or not

2)Hypothesis:

Null hypothesis: H0:$\mu 1=\mu 2$

Alternative hypothesis:H1:$\mu 1\neq \mu 2$

3) Hypothesis test:

Using Minitab statistical software

Two-Sample T-Test and CI: wheat, Maize

Two-sample T for wheat vs Maize

N Mean StDev SE Mean
wheat 12 5.625 0.717 0.21
Maize 12 6.767 0.959 0.28

Difference = μ (wheat) - μ (Maize)
Estimate for difference: -1.142
95% CI for difference: (-1.863, -0.421)
T-Test of difference = 0 (vs ≠): T-Value = -3.30 P-Value = 0.004 DF = 20

here 0.004<0.05 so we reject null hypothesis there is statistical difference between this two treatment

conclusion: Both Wheat and maize production are not equal

4) cohens d test:

Cohen's d = (M₂ - M₁) ⁄ SD_pooled

SD_pooled = √((SD₁² + SD₂²) ⁄ 2)

Cohen's d = (6.767 - 5.625) ⁄ 0.846691 = 1.348781.

95% confidence interval for wheat

95% Confidence Interval: 5.625 ± 0.406
(5.22 to 6.03)

"With 95% confidence the population mean is between 5.22 and 6.03, based on only 12 samples."

Short Styles:
5.625 (95% CI 5.22 to 6.03)
5.625, 95% CI [5.22, 6.03]

Margin of Error: 0.406
Sample Size: 12
Sample Mean: 5.625
Standard Deviation: 0.717
Confidence Level: 95%

95% confidence interval for maize

95% Confidence Interval: 6.767 ± 0.543
(6.22 to 7.31)

"With 95% confidence the population mean is between 6.22 and 7.31, based on only 12 samples."

Short Styles:
6.767 (95% CI 6.22 to 7.31)
6.767, 95% CI [6.22, 7.31]

Margin of Error: 0.543
Sample Size: 12
Sample Mean: 6.767
Standard Deviation: 0.959
Confidence Level: 95%