Question

We are continuing to study the difference in average time for completion for the two matching schemes. However, this time we had 30 individuals participate. The shapes and cutouts are all the same color (treatment s) The shapes and cutouts are different colors (treatment d) For each participant, the treatment s - treatment d was found. The 95% CI was (-4.617, -9.383). Complete the interpretation statement. "We are 95% confident that the time to completion for the same color method is between 4.617 to 9.383 than the different color method."

Answer 1

Answer:

We are 95% confident that the time to completion for the same color method is between 4.617 less to 9.383 less than the different color method.

Step-by-step explanation:

The (1 - α)% confidence interval for population parameter implies that there is a (1 - α) probability that the true value of the parameter is included in the interval.

Or, the (1 - α)% confidence interval for the parameter implies that there is (1 - α)% confidence or certainty that the true parameter value is contained in the interval.

The 95% confidence for the difference in the completion time of treatment is and d is,

CI = (-4.617, -9.383)

The parameter of the study is defined as:

treatment_s - treatment_d

Consider the 95% confidence interval, (-4.617, -9.383). The confidence interval consists of all negative values.

This implies that the difference between the completion time of treatment s and d is less than 0, i.e. the completion time of treatment s is less than that for treatment d.

Thus, the complete statement is:

"We are 95% confident that the time to completion for the same color method is between 4.617 less to 9.383 less than the different color method."

Answer 2

The complete statement is: we are 95% confident that the time to completion for the same color method is between 4.617 less to 9.383 less than the different color method.

The 95% confidence interval is given as:

$CI = (-4.617, -9.383)$

Where -4.617 represents the lower bound and -9.383 represents the upper bound

And the parameter of the study is treatment_s - treatment_d

Notice that the boundaries of the 95% confidence intervals are negative

This means that the difference between the completion time of both treatments is less than 0

The key word "less than 0" means that, the  complete statement is: we are 95% confident that the time to completion for the same color method is between 4.617 less to 9.383 less than the different color method.

Read more about confidence intervals at:

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