In your sample of 23 art students and 30 economics students, the mean amount that a group of economics students like statistics is 26, while the mean amount that a group of art students like statistics is 15. The variance in the economic group is 4.2, while the variance in the art group is 10.3.
Calculate your test statistic for finding whether the groups differ in how much they like statistics.
Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√n
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability that they will differ.
15.19
To calculate the test statistic for determining whether the groups differ in how much they like statistics, we can use the two-sample t-test formula. The test statistic formula for a two-sample t-test is given by:
t = (mean1 - mean2) / sqrt((var1/n1) + (var2/n2))
Where:
- mean1 is the mean of the first group (economics students) - 26
- mean2 is the mean of the second group (art students) - 15
- var1 is the variance of the first group (economics students) - 4.2
- var2 is the variance of the second group (art students) - 10.3
- n1 is the sample size of the first group (number of economics students) - 30
- n2 is the sample size of the second group (number of art students) - 23
Now, let's calculate the test statistic value:
t = (26 - 15) / sqrt((4.2/30) + (10.3/23))
t = 11 / sqrt(0.14 + 0.448)
t = 11 / sqrt(0.588)
t ≈ 11 / 0.767
t ≈ 14.34
Therefore, the test statistic for determining whether the groups differ in how much they like statistics is approximately 14.34.
To calculate the test statistic for determining if the groups differ in how much they like statistics, we can use the independent two-sample t-test. The formula for the test statistic is given by:
t = (mean1 - mean2) / sqrt((var1/n1) + (var2/n2))
Where:
mean1 = mean of the first group (economic students)
mean2 = mean of the second group (art students)
var1 = variance of the first group (economic students)
var2 = variance of the second group (art students)
n1 = number of observations in the first group (economic students)
n2 = number of observations in the second group (art students)
Let's plug in the given values:
mean1 = 26
mean2 = 15
var1 = 4.2
var2 = 10.3
n1 = 30 (number of economic students)
n2 = 23 (number of art students)
Substituting the given values into the formula, we have:
t = (26 - 15) / sqrt((4.2/30) + (10.3/23))
Now, let's calculate the test statistic:
t = 11 / sqrt(0.14 + 0.448)
Simplifying:
t = 11 / sqrt(0.588)
t = 11 / 0.7660
t ≈ 14.34
Therefore, the test statistic for determining if the groups differ in how much they like statistics is approximately 14.34.