You are conducting a study to test the hypothesis that there is a gender bias in
ID: 3131946 • Letter: Y
Question
You are conducting a study to test the hypothesis that there is a gender bias in perceptions of competence – specifically, that people assume men have more general ability than women. A sample of 10 college students is presented with photos of a female target and of a male target. Each participant rates both targets on a scale of 1 to 10, where higher scores represent greater general ability. The data are as follows:
Female Target
Male Target
1
6
8
8
5
6
6
8
7
9
6
7
5
6
6
6
7
8
4
4
(a)Subtracting the scores for the male target from those for the female target, what are H0 and Ha for this study?
(b)Compute tobt
(c)Should H0 be rejected? Why or why not? What can you conclude?
(d)Compute the 95% confidence interval.
(e)Compute the effect size.
(f)Draw a graph representing the data.
Female Target
Male Target
1
6
8
8
5
6
6
8
7
9
6
7
5
6
6
6
7
8
4
4
Explanation / Answer
t-test
Solution:
Answer (a)
We have to use the one sample t test for the population mean for checking the given claim or hypothesis. The null and alternative hypothesis for this test is given as below:
Null hypothesis: H0: There is no any significant difference in the average female target and average male target.
Alternative hypothesis: Ha: The average male target is greater than the average female target.
Symbolically, these hypotheses are written as below:
H0: µ1 - µ2 = 0 versus Ha: µ1 - µ2 < 0
The level of significance or the value of alpha is given as 0.05 or 5%.
Female Target
Male Target
Difference
1
6
-5
8
8
0
5
6
-1
6
8
-2
7
9
-2
6
7
-1
5
6
-1
6
6
0
7
8
-1
4
4
0
Answer (b)
The values for test statistic and p-value are given as below:
t Test for Hypothesis of the Mean
Data
Null Hypothesis m=
0
Level of Significance
0.05
Sample Size
10
Sample Mean
-1.3
Sample Standard Deviation
1.494434118
Intermediate Calculations
Standard Error of the Mean
0.4726
Degrees of Freedom
9
t Test Statistic
-2.7508
Answer c)
Lower-Tail Test
Lower Critical Value
-1.8331
p-Value
0.0112
Reject the null hypothesis
Here, we get the p-value as 0.0112 which is less than the given level of significance or alpha value 0.05, so we reject the null hypothesis that There is no any significant difference in the average female target and average male target. This means, we conclude that The average male target is greater than the average female target.
Answer d)
Here, we have to find the confidence interval for the average difference which is given as below:
Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation
1.4944
Sample Mean
-1.3
Sample Size
10
Confidence Level
95%
Intermediate Calculations
Standard Error of the Mean
0.472570774
Degrees of Freedom
9
t Value
2.2622
Interval Half Width
1.0690
Confidence Interval
Interval Lower Limit
-2.37
Interval Upper Limit
-0.23
Answer e)
Effect size = 1.0690
Answer f)
The scatter diagram for the female target and male target is given as below:
Female Target
Male Target
Difference
1
6
-5
8
8
0
5
6
-1
6
8
-2
7
9
-2
6
7
-1
5
6
-1
6
6
0
7
8
-1
4
4
0
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