Question

5. A study was conducted to determine whether the mean braking distance of four-cylinder cars is greater than the mean braking distance of six-cylinder cars. A random sample of 20 four-cylinder cars and a random sample of 20 six-cylinder cars were obtained, and the braking distances were measured.

(a) What would be the appropriate hypothesis test for this analysis?

(i) t-test for two independent samples

(ii) t-test for dependent samples

(iii) z-test for population mean

(iv) correlation

(b) Explain the rationale for your selection in (a). Specifically, why would this be the appropriate statistical approach

Answer 1

Solution:

Given:  A study was conducted to determine whether the mean braking distance of four-cylinder cars is greater than the mean braking distance of six-cylinder cars.

Sample Sizes:

n1 = sample size of  four-cylinder cars = 20

n2 = sample size of six-cylinder cars = 20

Part a) What would be the appropriate hypothesis test for this analysis?

(i) t-test for two independent samples

Part b) Explain the rationale for your selection in (a). Specifically, why would this be the appropriate statistical approach

We have two different samples collected braking distances of four-cylinder cars and braking distances of six-cylinder cars.

Thus we have two independent samples, we have to compare two means of two independent samples with small sample sizes with unknown standard deviations , so we must use t-test for two independent samples.

z test is used when population standard deviations are known and sample sizes are large.

t-test for dependent samples is used when samples or populations are dependent or pair of  observations are collected on same object.

correlation is used to test relationship between two correlated variables

Thus option ii) ,iii) and iv) are incorrect.