Question

You have been given the final results of this study. What are your conclusions? Describe your conclusions and how you derived them.

RQ: To what extent does our new composite material improve load-bearing capacity of aircraft wings?

Ha: Aircraft wings constructed with the new composite material will have greater load bearing capacity than aircraft wings that are not constructed with the new material.

H0: There is no difference between composite aircraft wing load bearing capacity and other aircraft wings.

Population 1: Aircraft wings constructed with a new composite material.

Population 2: Aircraft wings in general.

• Confidence Interval: 95%
• Population Mean = 59.945, Sample N=50, Sample X-bar=61, Sample SD=4, p=.034

Part I:

How the analysis was derived

Conclusion (Find each one)

Test that was conducted
Description of the data
Confidence interval selected
One or two tail test selected
T-critical value(s)
Test statistics (t-stat)
Decision to reject or not reject the null hypothesis by comparing the t-critical value to the test statistics
Statistically significant statement

Answer 1

Solution:

Here, we have to use one sample t test for the population mean.

H0: There is no difference between composite aircraft wing load bearing capacity and other aircraft wings.

Ha: Aircraft wings constructed with the new composite material will have greater load bearing capacity than aircraft wings that are not constructed with the new material.

H₀: µ = 59.945 versus H_a: µ > 59.945

This is a one tailed test. (upper tailed or right tailed)

We are given sample mean as Xbar = 61, sample standard deviation as S = 4, and sample size as n = 50.

The degrees of freedom is given as below:

df = n – 1 = 50 – 1 = 49

Confidence level = 95%

So, significance level = 5% or α = 0.05

Critical t value = 1.6766

(by using t-table)

Test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

t = (61 – 59.945)/[4/sqrt(50)]

t = 1.055/ 0.5657

t = 1.8650

Test statistic = 1.8650

Critical t value = 1.6766

Test statistic value is greater than critical value, so we reject the null hypothesis.

P-value = 0.0341

(by using t-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that Aircraft wings constructed with the new composite material will have greater load bearing capacity than aircraft wings that are not constructed with the new material.