Homework SourseIn a study to compare the IQ between boys and girls in a par
In a study to compare the IQ between boys and girls in a particular elementary school, a random sample of seventh grade boys and girls was taken from Vancouver Hill Elementary School. The girls and boys were asked to take an IQ test and their scores were recorded. Some summary statistics of the IQs of the boys and girls is given below.
Part a)
Which of the following test is appropriate for the comparison?
A. A two-sample t-test.
B. A paired t-test.
C. A z-test for a population proportion.
Part b)
In testing a hypothesis about the parameter of interest, what would your null hypothesis be?
A. There is no difference in the mean IQ for seventh grade boys and girls at Vancouver Hill Elementary School.
B. The difference between the mean IQ of seventh grade boys and girls is 1.6.
C. The mean difference between the IQ of a seventh grade boy at Vancouver Hill Secondary School and the IQ of a seventh grade girl at the same school is 1.6.
D. There is a difference in the mean IQ for boys and girls at Vancouver Hill Elementary School.
E. The mean IQ of seventh grade boys at Vancouver Hill Elementary School is greater than the mean IQ of seventh grade girls at the same school.
Part c)
If you use a 5% level of significance, which of the following would you conclude?
A. There is sufficient evidence to suggest that the mean difference between the IQ of a seventh grade boy at the school and the IQ of a seventh grade girl at the school is 1.6.
B. There is insufficient evidence to suggest that the mean difference between the IQ of a seventh grade boy at the school and the IQ of a seventh grade girl at the school is 1.6.
C. There is sufficient evidence to suggest that the mean IQ of seventh grade boys at the school is greater than the mean IQ of seventh grade girls at the school.
D. There is insufficient evidence to suggest that the mean IQ of seventh grade boys at the school is greater than the mean IQ of seventh grade girls at the school.
E. There is insufficient evidence to suggest that the difference between the mean IQ of seventh grade boys and girls at the school is 1.6.
F. There is sufficient evidence to suggest that there is a difference in the mean IQ for seventh grade boys and girls at the school.
G. There is sufficient evidence to suggest that the difference between the mean IQ of seventh grade boys and girls at the school is 1.6.
H. There is insufficient evidence to suggest that there is a difference in the mean IQ for seventh grade boys and girls at the school.
| Gender | Number of children measured | Average IQ | Standard deviations of IQ |
| Boys | 17 | 107.1 | 5.6 |
| Girls | 15 | 105.5 | 4.9 |
Solution
A.
OPTION A: A two sample t test.
As there are two independent samples here.
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B.
OPTION A. There is no difference in the mean IQ for seventh grade boys and girls at Vancouver Hill Elementary School.
Null hypotheses usually say \"no difference.\"
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C.
Formulating the null and alternative hypotheses,
Ho: u1 - u2 = 0
Ha: u1 - u2 =/= 0
At level of significance = 0.05
As we can see, this is a 2 tailed test.
Calculating the means of each group,
X1 = 107.1
X2 = 105.5
Calculating the standard deviations of each group,
s1 = 5.6
s2 = 4.9
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 17
n2 = sample size of group 2 = 15
Thus, df = n1 + n2 - 2 = 30
Also, sD = 1.856171476
Thus, the t statistic will be
t = [X1 - X2 - uD]/sD = 0.861989326
where uD = hypothesized difference = 0
Now, the critical value for t is
tcrit = 2.042272456
Thus, comparing t and tcrit, we decide to WE FAIL TO REJECT THE NULL HYPOTHESIS.
Also, using p values,
p = 0.395531543
Comparing this to the significance level, WE FAIL TO REJECT THE NULL HYPOTHESIS.
Thus, OPTION H: There is insufficient evidence to suggest that there is a difference in the mean IQ for seventh grade boys and girls at the school. [OPTION H, ANSWER]
