Question

BEYOND THE NUMBERS 2.201 LEARNING OUTCOMES 4 TO 7 A Challenging Interpretation Section Number:_ Name: original book page To be graded, all assignments must be completed and subnwitted on the EXHIBIT 1 A Common Problem researchers was interested in potential misinterpretations of the term A team of psychology confidence" in a confidence interval. They collected data from 442 undergraduate students, 34 graduate students, and 118 of their research-active colleagues. All subjects were presented with a "fictitious scenario of a professor who conducts an experiment and reports a 95% a for the (population proportion that ranges from 0.1 to 0.4. Neither the topic of study nor the underlying statistical model used to compute the Cl was specified in the survey." The subjects were then asked to specify whether they agreed or disagreed with each of the following statements as interpretations found. of that confidence interval (CI). Here is what the investigators TABLE 2.7 Percentage of Subjects Agreeing with the Statement* First Year Master Students Students Researchers (n 442)(n 34) n 118) 1. The probability that the true proportion is greater than O 2. The probability that the true proportion equals O is 3. There is a 95% probability that the true proportion lies 51% 32% isat least 95%. 55% smaller than 5%. 58% 50% 59% between 0.1 and 0.4 We can be 95% confident that the true proportion lies between 0.1 and 04 50% 55% If we were to repeat the experiment over and over, then 95% of the time the true porportion falls between 0.1 and 0.4. 5. 66% 79% 58% 2014. htpllwwweagrs.comnrsoekstaAPeR pdt Tablie has been reformatted,one statement emimed,and mean changed to proportion throghout All of the statements are wrongl Students and professional researchers alike found the interpretation of a confidence interval to be challenging. Yet, it is not acceptable to step away from this challenge. Confidence intervals are used everywhere as a kind of statistical seal of approval for survey and experiment results. 181 BEYOND THE NUMBERS 2.20

Answer 1

1.

The statement has used the wrong bound on true proportion. It should be [0.1-0.4]. Also, the Confidence interval is not a probability of population parameter, it is a probability statement about the confidence interval.

2.

The statement has used the wrong bound on true proportion. It should be anything except [0.1-0.4]. Also, the Confidence interval is not a probability of population parameter, it is a probability statement about the confidence interval.

3.

Confidence interval is not a probability of population parameter, it is a probability statement about the confidence interval. Once an interval is calculated, this interval either covers the parameter value or it does not; it is no longer a matter of probability.

4.

If a confidence interval is calculated, we are 100% confident that interval either covers the parameter value or it does not.

5.

The fraction of calculated confidence intervals (which would differ for each sample) that encompass the true population parameter would tend toward 95%. Every confidence interval doesn't need to be [0.1-0.4].

Please upvote if you have liked my answer, would be of great help. Thank you