Find the value of t for the difference between two means based on an assumption of normality and this information about two samples. (Use sample 1 - sample 2. Give your answer correct to two decimal places.)
Sample Number Mean Std. Dev.
1 25 38.6 13.7
2 29 42.1 10.2
t= (38.6-421)/sqrt (13.7^2/25 + 10.2^2/29))
I came up with -114.80229
There was typo
t= (38.6-42.1)/sqrt (13.7^2/25 + 10.2^2/29))
t = -1.05
To find the value of t for the difference between two means based on an assumption of normality, you will need to calculate the t-statistic. The formula for the t-statistic is:
t = (mean1 - mean2) / sqrt((s1^2 / n1) + (s2^2 / n2))
Where:
mean1 and mean2 are the means of the two samples,
s1 and s2 are the standard deviations of the two samples,
n1 and n2 are the sample sizes of the two samples.
Let's plug in the given values into the formula:
mean1 = 38.6
mean2 = 42.1
s1 = 13.7
s2 = 10.2
n1 = n2 = 25 (assuming equal sample sizes)
t = (38.6 - 42.1) / sqrt((13.7^2 / 25) + (10.2^2 / 25))
= -3.5 / sqrt((187.69 / 25) + (104.04 / 25))
= -3.5 / sqrt(7.51 + 4.16)
= -3.5 / sqrt(11.67)
≈ -3.5 / 3.412
Now, divide -3.5 by 3.412 to get:
t ≈ -1.026 (rounded to two decimal places)
Therefore, the value of t for the difference between the two means is approximately -1.03 (rounded to two decimal places).