Data indicates that adolescent girls tend to experience a drop in self-esteem. To evaluate this result, a researcher obtains a sample of N = 36 adolescent girls, all 13 years old. A self-esteem measure is administered to each participant and the average score for the sample is X =68. It is known that the distribution of self-esteem scores for the population of pre-teen girls is normal with mean 80 and standard deviation 10. (a) Compute a 95% confidence interval for µ, the population mean self-esteem score for adolescent girls. (b) Compute Cohen’s d to estimate the size of the described effect. (c) Perform a hypothesis test to decide whether the mean self-esteem score for adolescent girls is significantly different from the mean self-esteem score for pre-teen girls.
Data indicates that adolescent girls tend to experience a drop in self-esteem. To evaluate this result, a researcher obtains a sample of N = 36 adolescent girls, all 13 years old. A self-esteem measure is administered to each participant and the average score for the sample is X =68. It is known that the distribution of self-esteem scores for the population of pre-teen girls is normal with
(a) Compute a 95% confidence interval for µ, the population mean self-esteem score for adolescent girls.
(b) Compute Cohen’s d to estimate the size of the described effect.
(c) Perform a hypothesis test to decide whether the mean self-esteem score for adolescent girls is significantly different from the mean self-esteem score for pre-teen girls.
(d) Compute and interpret a Bayes factor for the model (either H0 or H1) with the best predictive adequacy.
(e) Compute and interpret the posterior model probability for the winning model chosen in part (d).
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