Find the 95% confidence interval for the difference between two means based on this information about two samples. Assume independent samples from normal populations. (Use conservative degrees of freedom.) (Give your answers correct to two decimal places.)
Sample Number Mean Std. Dev.
1 27 39 21
2 16 26 35
Lower Limit Incorrect: Your answer is incorrect. .
Upper Limit Incorrect: Your answer is incorrect. .
This is what I have got so far. (27-1)X21squared + (16-1) X35squared divided by 27+16-2=12160.55556 then I sqrt 1/27 + 1/16=.3154949081, then 39-26/? x.315494981 now I am stuck???
Is that two table or one table
(-7.02, 33.02)
It is a 2 samples, those answers are not right, but I desperately need your help. I do appreciate your help.
I am sorry those answers were right, I was putting them on another proboem that I have, and I need your help on it, my sample 1 Number is 22, mean 31, and Std dev. 28, Second sample is Number 25, mean 25, Std. Dev. 35. I get as far as I did on the one above and that is as far as I can go. Thank goodness this is the last problem like this to do. Confidence 98%. Again thank you
To find the 95% confidence interval for the difference between two means, you can use the following formula:
Confidence Interval = (X1 - X2) ± t * sqrt((s1^2 / n1) + (s2^2 / n2))
X1 and X2 are the means of the samples, s1 and s2 are the standard deviations, n1 and n2 are the sample sizes, and t is the critical value from the t-distribution based on the desired confidence level and degrees of freedom.
First, let's calculate the critical value. Since the sample sizes are small and the degrees of freedom are conservative, we can use the more conservative t-distribution. For a 95% confidence level and conservative degrees of freedom, the critical value is approximately 2.044.
Next, substitute the values into the formula:
X1 = 27
X2 = 16
s1 = 21
s2 = 35
n1 = 39
n2 = 26
t = 2.044
Confidence Interval = (27 - 16) ± 2.044 * sqrt((21^2 / 39) + (35^2 / 26))
Now, let's calculate this:
Confidence Interval = 11 ± 2.044 * sqrt((441 / 39) + (1225 / 26))
Confidence Interval = 11 ± 2.044 * sqrt(11.31 + 47.12)
Confidence Interval = 11 ± 2.044 * sqrt(58.43)
Calculating the square root:
Confidence Interval = 11 ± 2.044 * 7.64
Confidence Interval = 11 ± 15.62
Finally, the 95% confidence interval for the difference between two means is:
Lower Limit = 11 - 15.62 = -4.62
Upper Limit = 11 + 15.62 = 26.62
Therefore, the correct confidence interval is -4.62 to 26.62.