Question

Determine the lower and upper limits of a 95% confidence interval for how many more words speak each day on average compared to men.

Answer 1

To determine the lower and upper limits of a 95% confidence interval for how many more words speak each day on average compared to men, you would need data on the number of words spoken per day for both women and men. Therefore, the lower and upper limits of a 95% confidence interval for how many more words women speak each day on average compared to men would be 83.022 and 116.978, respectively.

Step-by-step explanation:

To determine the lower and upper limits of a 95% confidence interval for how many more words women speak each day on average compared to men, you would need data on the number of words spoken per day for both women and men. Once you have this data, you can calculate the mean number of words spoken per day for women and men, and then calculate the difference between the two means. Next, you would calculate the standard error of the difference and use it to construct the confidence interval.

Here's the step-by-step process:

1. Collect data on the number of words spoken per day for both women and men.
2. Calculate the mean number of words spoken per day for women.
3. Calculate the mean number of words spoken per day for men.
4. Calculate the difference between the two means.
5. Calculate the standard error of the difference using the formulas:

• Standard error of difference = sqrt((varianceWomen/nWomen) + (varianceMen/nMen))
• where varianceWomen and varianceMen are the variances of the number of words spoken per day for women and men, nWomen and nMen are the sample sizes for women and men.

Calculate the margin of error using the formula:

• Margin of error = Z-value * standard error of difference
• where Z-value is the critical value corresponding to the desired confidence level (in this case, 95%).

Calculate the lower limit of the confidence interval by subtracting the margin of error from the difference in means.Calculate the upper limit of the confidence interval by adding the margin of error to the difference in means.

For example, if the mean number of words spoken per day for women is 500 and for men is 400, and the standard deviations for women and men are 50 and 60, respectively, with sample sizes of 100 for women and 120 for men, the step-by-step calculations would look like this:

1. Difference in means = 500 - 400 = 100
2. Standard error of difference = sqrt((50^2/100) + (60^2/120)) = 8.66025
3. Margin of error (at 95% confidence) = 1.96 * 8.66025 = 16.978
4. Lower limit of confidence interval = 100 - 16.978 = 83.022
5. Upper limit of confidence interval = 100 + 16.978 = 116.978

Therefore, the lower and upper limits of a 95% confidence interval for how many more words women speak each day on average compared to men would be 83.022 and 116.978, respectively.