Question

Independent random samples of 36 and 45 observations are drawn from two quantitative populations, 1 and 2, respectively. The sam- ple data summary is shown here:

Sample 1

36

Sample 2

15

1.31

Sample Size Sample Mean

1.21

Sample Variance

0.056

0.051

Do the data present sufficient evidence to indicate that the mean for population 1 is smaller than the mean for population 2? Use the p-value approach and test at the 2% significance level.

Answer 1

Answer: you can analyze the given data and determine whether there is sufficient evidence to indicate that the mean for population 1 is smaller than the mean for population 2.

Step-by-step explanation:

To determine if the mean for population 1 is smaller than the mean for population 2, we can conduct a hypothesis test using the p-value approach.

Step 1: State the null and alternative hypotheses.

The null hypothesis, denoted as H0, assumes that the mean for population 1 is equal to or greater than the mean for population 2. The alternative hypothesis, denoted as Ha, assumes that the mean for population 1 is smaller than the mean for population

2.Set the significance level.

The significance level, denoted as α, is given as 2%. This means that we will reject the null hypothesis if the p-value is less than 0.02.

3.Calculate the test statistic.

We will use a t-test since we are comparing the means of two independent populations.