Question

Hi there, I just need help with the last couple sub parts of this question. I'm having a difficult time understanding this. Can somebody help me please?

Below is the data for a personality questionnaire measuring conscientiousness. These data were taken from a random sample of 16 undergraduate psychology majors. In the general population, scores on this questionnaire are normally distributed with a mean (μ) of 50. You hypothesize that this sample is not representative of the general population. Specifically, you hypothesize that psychology students form a distinct sub-population, with DIFFERENT conscientiousness, relative to the general population. That is, it would be equally interesting to find out they have higher or lower conscientiousness. Conduct a one-sample t-test by answering the following questions.

Data: N = 16, xbar (sample mean) = 55.100, S_x = 7.17

f. Calculate and interpret the 95% Confidence interval

g. Calculate and interpret the standardized effect size (Cohen's d).

h. What do you conclude about your research question (use your own words, in everyday language)

Answer 1

f)

Given,

Mean (xbar) = 55.100

Sample Std Dev(s) = 7.17

n = 16

Sample Std Error (SE) = s/n^1/2 = 1.79

At alpha = 0.05,

Z_Critical = 1.96

Hence, 95% CI = Mean +/- Z_Critical * SE = 55.1 +/- 1.96*1.79 = {51.59,58.61}

95% CI represents that there is 95% probability that the true mean lies in the interval {51.59,58.61}

g)

Effect Size (d) = (µ- µ₀)/σ

where μ represents the mean of the population of interest and μ₀ represents a value to which the mean is to be compared. If the standard deviation is σ

A d near 0.2 is a small effect, a d near 0.5 is a medium effect, and a d near 0.8 is a large effect.

d cannot be calculated as complete information is not provided.