Question

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 fourcylinder 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

Answer 1

Answer:

a) t-test for two independent samples

b) For this case we have two different samples and both are less than 30 and we don't have any info about the populationd deviation's. So for this case the most appropiate test is the t-tes for two independent samples

Step-by-step explanation:

The independent t-test, is known as two sample t-test or independent-samples t-test, is an statistical test used to " determines whether there is a statistically significant difference between the means in two unrelated groups"

The system of hypothesis could be on this case like this:

Null hypothesis: $\mu_1 = \mu_2$

Alternative hypothesis: $\mu_1 \neq \mu_2$

Or equivalently:

Null hypothesis: $\mu_1 - \mu_2 = 0$

Alternative hypothesis: $\mu_1 -\mu_2 \neq 0$

The statistic to check the hypothesis is given by:

$t=\frac{(\bar X_1 -\bar X_2)-(0)}{\sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}}$

And this statistic follows a t distribution with degrees of freedom $df=n_1 +n_2 -2$

We can check the hypothesis using the p value method or the critical approach, but we need to have a significance level.

Part a

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?

For this case we have two different samples and both are less than 30 and we don't have any info about the populationd deviation's. So for this case the most appropiate test is the t-test for two independent samples