A random sample of females was observed to exhibit a lower average level of self-esteem than a random sample of males.To assess the likelihood that this observed difference reflects a real difference in the average self-esteem of the total population of males and females,you should
A) construct a bar graph.
B) calculate the correlation.
C) plot the distribution of self-esteem levels among all males and females.
D) conduct a test of statistical significance.

Question

Quizplus · Accepted Answer

To assess the likelihood of a real difference, a statistician would need to conduct a statistical hypothesis test to determine if the observed difference in self-esteem between the two samples is statistically significant. This would require calculating a p-value, which would estimate the probability of observing the sample difference under the assumption that there is no real difference in self-esteem between males and females in the population. If the p-value is low enough (typically less than 0.05), we reject the null hypothesis (that there is no true difference) and conclude that the observed difference is likely due to a real difference in self-esteem levels between males and females in the population. A bar graph or correlation would not provide sufficient information to make this determination. Plotting the distribution of self-esteem levels would not be necessary for conducting the statistical test, though it could be useful for understanding the nature of the difference if it is found to be statistically significant.

A Random Sample of Females Was Observed to Exhibit a Lower