Researchers conduct a study to estimate the proportion of participants who respond positively to cognitive behavioral therapy; they find that 35.4% of participants responded positively with a 95% CI from 19.5% to 51.3%. Which of the following interpretations of their confidence interval is incorrect? Group of answer choices We are 95% confident that the true population proportion of positive response to cognitive behavioral therapy is somewhere between 19.5% and 51.3%. There is a 95% chance that the population proportion of positive response to cognitive behavioral therapy is somewhere between 19.5% and 51.3%. A range of plausible values for the population proportion of positive response to cognitive behavioral therapy is from 19.5% and 51.3%. The probability that this constructed confidence interval contains the true population proportion of positive response to cognitive behavioral therapy is either 0% or 100%. All of the above are correct interpretations.
Added by Daniel T.
Step 1
Option 1 correctly states this interpretation. Option 2 is incorrect because it implies that the confidence interval is a probability statement about the population parameter, which is not true. The true population parameter is fixed and unknown, and the Show more…
Show all steps
Close
Your feedback will help us improve your experience
Keondre Parker and 55 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A study was done to compare the effectiveness of cognitive behavioral therapy (CBT) to dialectic behavior therapy (DBT) for treating anxiety related conditions. Scoring of effectiveness was done by participating therapists on a scale from 0 to 100. Of 23 cases under CBT, effectiveness had sample mean 58.775, sample standard deviation 11.564, and 5-number summary 6 | 47 | 61 | 68 | 77. Of 18 cases under DBT, effectiveness had sample mean 52.311, sample standard deviation 7.013, and 5-number sum- mary 35 | 46 | 53 | 57 | 64. a) Interval estimate: Find the point estimate of the difference in population means of effectiveness under each therapy. Find the standard error of this estimate. Find the margin of error for a 95% confidence interval of the difference in population means, and report the 95% confidence interval. b) Use a two-sided hypothesis test on the claim that the two therapies differ in their effectiveness. (i) State hypotheses (ii) State and assess the validity of the distribution assumptions (iii) Calculate the test statistic (iv) Calculate the p-value (v) Using a 0.05 significance level, do you reject the null hypothesis or not? What is this decision in the context of the problem? c) Interpret the confidence interval in part (a). Describe the consistency or discrepancy between the confidence interval and the conclusion of the test. If there is a discrepancy, what caused it ?
Dominador T.
A psychologist is interested in constructing a 95% confidence interval for the proportion of people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain. 74 of the 776 randomly selected people who were surveyed agreed with this theory. Round answers to 4 decimal places where possible. a. With 95% confidence the proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain is between [box] and [box]. b. If many groups of 776 randomly selected people are surveyed, then a different confidence interval would be produced from each group. About [box] percent of these confidence intervals will contain the true population proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain and about [box] percent will not contain the true population proportion.
Joanna Q.
A psychologist is interested in constructing a 95% confidence interval for the proportion of people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain. 54 of the 777 randomly selected people who were surveyed agreed with this theory. a. With 95% confidence the proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain is between and . b. If many groups of 777 randomly selected people are surveyed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain and about percent will not contain the true population proportion.
Steve G.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD