Answer:
There is enough evidence to claim that population mean 1 is less than population 2 at the 0.05 significance level.
Step-by-step explanation:
We are given the following in the question:
Group 1:
Group 2:
Alpha, α = 0.05
First, we design the null and the alternate hypothesis
Since, the population variances are equal and that the two populations are normally distributed, we use t-test(pooled test) for difference of two means.
Formula:
Pooled standard deviation
Putting all the values we get:
Now,
Since,
We fail to accept the null hypothesis and reject the null hypothesis. We accept the alternate hypothesis.
We conclude that the mean score for Group 1 is significantly lower than the mean score for Group 2.
There is enough evidence to claim that population mean 1 is less than population 2 at the 0.05 significance level.