Numerous studies have found that males report higher

self-esteem than females, especially for adolescents
(Kling, Hyde, Showers, & Buswell, 1999). Typical
results show a mean self-esteem score of M � 39.0 with
SS � 60.2 for a sample of n � 10 male adolescents and
a mean of M � 35.4 with SS � 69.4 for a sample of
n � 10 female adolescents.
a. Do the results indicate that self-esteem is
significantly higher for males? Use a one-tailed
test with � � .01.
b. Use the data to make a 95% confidence interval
estimate of the mean difference in self-esteem
between male and female adolescents.
c. Write a sentence demonstrating how the results
from the hypothesis test and the confidence interval
would appear in a research report.

a. To determine if the results indicate that self-esteem is significantly higher for males, we can conduct a t-test.

Step 1: Set up the hypotheses:
Null hypothesis (H0): The mean self-esteem scores for males and females are equal.
Alternative hypothesis (Ha): The mean self-esteem score for males is significantly higher than females.

Step 2: Determine the level of significance (α):
The given level of significance is α = 0.01.

Step 3: Conduct the t-test:
Calculate the t-value using the formula:
t = (M1 - M2) / sqrt((SS1/n1) + (SS2/n2))
where
M1 = mean self-esteem score for males
M2 = mean self-esteem score for females
SS1 = sum of squares for males
SS2 = sum of squares for females
n1 = sample size of males
n2 = sample size of females

t = (39.0 - 35.4) / sqrt((60.2/10) + (69.4/10))
t = 3.6 / sqrt(6.02 + 6.94)
t ≈ 3.6 / sqrt(13.96)
t ≈ 3.6 / 3.73
t ≈ 0.965

Step 4: Determine the critical value:
The critical value for a one-tailed test at α = 0.01 with 18 degrees of freedom is 2.552.

Step 5: Compare the t-value with the critical value:
Since the calculated t-value (0.965) is less than the critical value (2.552), we fail to reject the null hypothesis.

Step 6: Draw a conclusion:
Based on the results, we do not have enough evidence to support the claim that self-esteem is significantly higher for males.

b. To make a 95% confidence interval estimate of the mean difference in self-esteem between male and female adolescents, we can use the formula:

CI = (M1 - M2) ± t * sqrt((SS1/n1) + (SS2/n2))
where CI = confidence interval,
t = t-value for the desired level of confidence (95% confidence level is typically associated with a t-value of 2.262),
M1 = mean self-esteem score for males,
M2 = mean self-esteem score for females,
SS1 = sum of squares for males,
SS2 = sum of squares for females,
n1 = sample size of males,
n2 = sample size of females.

CI = (39.0 - 35.4) ± 2.262 * sqrt((60.2/10) + (69.4/10))
CI = 3.6 ± 2.262 * sqrt(6.02 + 6.94)
CI = 3.6 ± 2.262 * sqrt(13.96)
CI ≈ 3.6 ± 2.262 * 3.73
CI ≈ 3.6 ± 8.44

The 95% confidence interval estimate of the mean difference in self-esteem between males and females is approximately (-4.84, 12.04).

c. A sentence demonstrating how the results from the hypothesis test and the confidence interval would appear in a research report could be:
"The results of the one-tailed t-test indicated that there was not significant evidence to suggest that self-esteem is higher for males compared to females (t = 0.965, df = 18, p > 0.01). Additionally, a 95% confidence interval estimate of the mean difference in self-esteem between male and female adolescents ranged from -4.84 to 12.04, suggesting that the true mean difference could fall within this range."