. Using the central limit theorem, construct a 95% confidence interval for the average total cry time for infants in the control group and infants in the intervention group. For this question only, assume that the standard deviation of cry time within each group is known and is equal to 22 seconds.
Control
Lower Bound
unanswered
Upper Bound
unanswered
Intervention
Lower Bound
unanswered
Upper Bound
To construct a 95% confidence interval for the average total cry time for infants in the control group and intervention group using the central limit theorem, we need to follow a few steps.
Step 1: Calculate the sample mean for each group.
The sample mean for the control group and intervention group can be calculated by taking the average of all the cry time values in each group.
Step 2: Calculate the standard error.
The standard error measures the variability of the sample mean. It can be calculated by dividing the standard deviation by the square root of the sample size. In this case, since the standard deviation within each group is known and equal to 22 seconds, we can use it to calculate the standard error.
Step 3: Determine the critical value.
Since we want a 95% confidence interval, we need to find the critical value associated with the desired confidence level. For a 95% confidence level, the critical value is approximately 1.96.
Step 4: Calculate the margin of error.
The margin of error can be calculated by multiplying the standard error by the critical value.
Step 5: Calculate the lower and upper bounds.
To calculate the lower and upper bounds, subtract and add the margin of error to the sample mean, respectively.
Now let's calculate the confidence intervals for each group:
Control:
Sample mean: Let's assume the sample mean of the control group is 100 seconds.
Standard error: 22 / √(sample size)
Critical value: 1.96
Margin of error: standard error * critical value
Lower bound: sample mean - margin of error
Upper bound: sample mean + margin of error
By plugging in the values, you can calculate the lower and upper bounds of the confidence interval for the control group.
Intervention:
Follow the same steps as above, but replace the sample mean with the intervention group's sample mean.
Remember, the sample means and sample sizes need to be provided to calculate the confidence interval accurately.