1. Hypotheses Testing

Having a little trouble with some of the below

Following the introduction of a new initiative to improve the time taken to clear motorway incidents, a random sample of 8 damage only incidents was analysed. It was found that the mean time to clear the carriageway was 22 minutes and the standard deviation was 12 minutes. Before the new initiative was introduced, an analysis of 35 incidents showed that the mean time to clear the carriageway was 28 minutes, with a standard deviation of 17 minutes. Test whether there has been a significant decrease in the mean time to clear the carriageway following damage only incidents following introduction of the new initiative.

Clearly state the statistical assumptions, hypothesis, significance level and p-value for your test.

cheers for any help

2. Re: Hypotheses Testing

You are looking for a t-test for the difference in means. One tailed test.

Let $\mu_1$ be the population mean of the sample $n_1=8, \bar{x}_1 = 22, s= 12$ and

let $\mu_2$ be the population mean of the sample $n_2=35, \bar{x}_2 = 38, s= 17$

$H_0: \mu_1 < \mu_2$

$H_a: \mu_1 \geq \mu_2$

Give this article a read (problem 2 in particular) to help find the test statistic, degrees of freedom and critical value.

Hint: In your case the difference in means is zero.

Reject $H_0$ if $|t_{calc}| > |t_{crit}|$

I suggest you test your hypothesis at $\alpha = 0.05$

3. Re: Hypotheses Testing

Is there an article missing here?