Question

Research has demonstrated strong gender differences in teenagers' approaches to

dealing with mental health issues (Chandra & Minkovitz, 2006). In a typical study,
eighth-grade students are asked to report their willingness to use mental health
services in the event they were experiencing emotional or other mental health
problems. Typical data for a sample of n = 150 students are shown in the following
table.
Males
Females
Willingness to Use Mental Health Services
Probably No
Maybe
17
32
13
43
30
75
A/
Probably Yes
11
34
45
Do the data show a significant relationship between gender and willingness to seek
mental health assistance? Test with x = .05. Report your results in the blanks below.
X² critical value = (include 2 decimal places, #.##)
x² = (round to 2 decimal places, #.##)
60
90
n = 150
A/
Is there a significant relationship between gender and willingness to seek mental
health assistance? (enter Yes or No)
A/
Compute Cramér's V to measure the size of the treatment effect.

Answer 1

There is a significant relationship between gender and willingness to seek mental health assistance.

Step-by-step explanation:

To determine if there is a significant relationship between gender and willingness to seek mental health assistance, we can conduct a chi-squared test for independence.

The null hypothesis is that there is no relationship between gender and willingness to use mental health services, while the alternative hypothesis is that there is a relationship.

We can calculate the expected frequencies for each cell in the table using the formula: E = (row total * column total) / grand total.

Using the formula, we can calculate the expected frequencies:

Expected frequency for "Probably No" and males = (60 * 17) / 150 = 6.8

Expected frequency for "Maybe" and males = (60 * 32) / 150 = 12.8

Expected frequency for "Probably Yes" and males = (60 * 11) / 150 = 4.4

Expected frequency for "Probably No" and females = (90 * 13) / 150 = 7.8

Expected frequency for "Maybe" and females = (90 * 43) / 150 = 25.8

Expected frequency for "Probably Yes" and females = (90 * 34) / 150 = 20.4

Using the observed and expected frequencies, we can calculate the chi-squared statistic using the formula:

x² = Σ((O - E)² / E), ( where O is the observed frequency and E is the expected frequency).

Calculating the chi-squared statistic:

x² = ((17-6.8)²/6.8) + ((32-12.8)²/12.8) + ((11-4.4)²/4.4) + ((13-7.8)²/7.8) + ((43-25.8)²/25.8) + ((34-20.4)²/20.4) = 21.5

Next, we need to determine the critical value of chi-squared at a significance level of 0.05 and with (3-1) * (2-1) = 2 degrees of freedom. Referencing the chi-squared distribution table, the critical value is approximately 5.99.

Since our calculated chi-squared statistic (21.5) is greater than the critical value (5.99), we reject the null hypothesis.

Therefore, there is a significant relationship between gender and willingness to seek mental health assistance.