STAT 340 Consider that a researcher conducted a study

| March 14, 2016

Question
Consider that a researcher conducted a study that examined resilience attitudes of 100 women, who participated in an educational intervention over time. The variable “resilience” was measured by a Likert scale with 30 items statements; each scaled on 1 to 5 points. The point of “1” meant the lowest level of resilience, while the point of “5” meant the highest resilience. A higher total score was interpreted as “higher level of resilience.”

The researcher first measured the resilience of these women before they entered the educational intervention as a pre-test, and found that at pre-test, the resilience scores were normally distributed with a Mean = 85 and Standard Deviation (SD) = 2.5.

[Hint – please keep in mind the rules on “normal distribution” when figuring out the questions, and you may want to review slides on hypothesis testing as well]

Answer the following set of questions based on rules governing the normal distribution of scores.

(a) What was the median resilience score for these women at pre-test, and why?

(b) What was the modal resilience score for these women at pre-test, and why?

(c) What were the two scores of resilience between which 95% of women scored at this pre-test? Please explain/show how you calculated/derived these two scores:

(d) Consider that “Anna” is one such participating woman, and Anna scored 1SD below the mean at pre-test. Please indicate Anna’s score on resilience, and explain/show how you calculated/derived her score:

(d) Consider that “Shakila” is another woman, whose reliance scores were collected at pre-test, and she actually scored 1SD above the mean in her pre-test resilience. What percent of participating women had resilience scores between Anna and Shakila, and briefly explain how you derived your answer:

(e) Consider that Anna scored 1 SD below the mean in her resilience, and Shakila scored 1 SD above the mean in her resilience. At what percentile for resilience did each woman score on the pre-test? Explain and show how you calculated/derived your answer.

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