Can someone tell me what formula I should use?
The number of milligrams of tar in filtered and unfiltered cigarettes is being compared. The following cigarettes are pulled to be part of the samples:
Filtered: bunch of data
Unfiltered: bunch of data
The first question is create a confidence interval of the difference between the two types of cigarettes.
Thanks
To create a confidence interval for the difference between the two types of cigarettes, you would need to use the appropriate formula based on your sample data. In this case, since you have two independent samples (filtered and unfiltered cigarettes) and you want to compare the means of these two samples, you can use the two-sample t-test formula.
The formula for the confidence interval for the difference between two means is as follows:
Confidence Interval = (X1 - X2) ± (t * SE)
Where:
- X1 and X2 are the means of the two samples (filtered and unfiltered cigarettes).
- t is the critical value from the t-distribution, which depends on the desired confidence level and the degrees of freedom.
- SE is the standard error, which is calculated as the square root of [(s1²/n1) + (s2²/n2)], where s1 and s2 are the sample standard deviations of the two samples, and n1 and n2 are the sample sizes.
Here are the steps to calculate the confidence interval:
1. Calculate the sample means (X1 and X2) for the filtered and unfiltered cigarettes.
2. Calculate the sample standard deviations (s1 and s2) for the filtered and unfiltered cigarettes.
3. Determine the sample sizes (n1 and n2) for the filtered and unfiltered cigarettes.
4. Calculate the standard error (SE) using the formula SE = sqrt[(s1²/n1) + (s2²/n2)].
5. Determine the degrees of freedom using the formula DF = n1 + n2 - 2.
6. Look up the critical value (t) corresponding to your desired confidence level and the degrees of freedom.
7. Substitute the values into the confidence interval formula and calculate the lower and upper bound of the interval.
Note: The confidence level determines the degree of certainty you want in your estimation. Common confidence levels are 90%, 95%, and 99%.
Remember to consult with a statistician or refer to your statistical software for specific calculations and interpretation of the results.