a sample of 120 men and women randomly divided into 3 groups with 40 people per group. group 1 members varied their workouts. group 2 performed the same exercise at each workout. group 3 had no set schedule or regulations for their workouts. by the end of the study 18 people had dropped out of the first exercise group. estimate the dropout rate for exercises who vary their routine using a 95% confidence interval
it's not 18/40 to find p.
18/40 to find p .45+/-1.96 square of (.45)(.55)/40
:)
To estimate the dropout rate for individuals who vary their workout routine, we can calculate a confidence interval using the provided data. Here's how we can do it step by step:
Step 1: Calculate the proportion of dropouts in Group 1
The total number of people in Group 1 is 40. Given that 18 people dropped out, we can calculate the proportion as follows:
Dropout rate (Group 1) = 18 / 40 = 0.45
Step 2: Calculate the standard error
To calculate the standard error, we need the sample size of Group 1. Since there were initially 40 people in each group, the sample size remains the same after the dropouts. Hence, we can use 40 as the sample size.
Standard Error (SE) = sqrt((dropout rate * (1 - dropout rate)) / sample size)
SE = sqrt((0.45 * (1 - 0.45)) / 40)
Step 3: Calculate the margin of error
To calculate the margin of error, we need to determine the critical value based on the desired confidence level. In this case, we want a 95% confidence interval. Looking up the critical value for a 95% confidence interval in a standard normal distribution table, we find the value to be approximately 1.96.
Margin of Error = critical value * SE
Margin of Error = 1.96 * SE
Step 4: Calculate the lower and upper bounds
Using the margin of error, we can calculate the lower and upper bounds of the confidence interval.
Lower Bound = dropout rate - margin of error
Upper Bound = dropout rate + margin of error
Step 5: Calculate the confidence interval
Confidence Interval = Lower Bound, Upper Bound
Plug in the values from Steps 1-4 to calculate the confidence interval for the dropout rate.