Question

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.

Gender	Number of children measured	Average IQ	Standard deviations of IQ
Boys	17	107.1	5.6
Girls	15	105.5	4.9

Part a) What is the parameter of interest in this study?

The difference in the mean IQ of seventh grade grade boys and girls at Vancouver Hill Elementary School.
The difference in the mean IQ of the children taken in the sample from Vancouver Hill Elementary School.
The mean IQ of boys and girls at Vancouver Hill Elementary School.
The difference in the variances of IQ of the boys and girls taken in the sample from Vancouver Hill Elementary School.
The mean IQ of children at elementary schools in Canada.

Part b) Based on the data provided, what is your estimate of this parameter?  

Part c) In testing a hypothesis about the parameter of interest, what would your null hypothesis be?

There is a difference in the mean IQ for boys and girls at Vancouver Hill Elementary School.
There is no difference in the mean IQ for seventh grade boys and girls at Vancouver Hill Elementary School.
The difference between the mean IQ of seventh grade boys and girls is 1.6.
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.
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 d) You would take the alternative hypothesis to be:

two-sided
one-sided, left-tailed
one-sided, right-tailed
it does not matter whether we take a one-sided or two-sided alternative

Part e) Which of the test statistics (A - D) you would choose to test your hypotheses?  ? A B C D  

A		?0=?¯−?0?/?√z0=y¯−μ0σ/n		B		?0=?¯1−?¯2SE(?¯1−?¯2)t0=y¯1−y¯2SE(y¯1−y¯2)
C		?0=?¯??/?√t0=d¯sd/n		D		?0=?¯−?0?/?√t0=y¯−μ0s/n

Part f) If you use a 5% level of significance, which of the following would you conclude?

There is sufficient evidence to suggest that there is a difference in the mean IQ for seventh grade boys and girls at the school.
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.
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.
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.
There is insufficient evidence to suggest that there is a difference in the mean IQ for seventh grade boys and girls at the school.
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.
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.
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.

Answer 1

Ans:

a)

The difference in the mean IQ of seventh grade grade boys and girls at Vancouver Hill Elementary School.

b)Point estimate=107.1-105.5=1.6

c)There is no difference in the mean IQ for seventh grade boys and girls at Vancouver Hill Elementary School.

d)two-sided

e)Option B is correct.

f)Test statistic:

t=(107.1-105.5)/SQRT((5.6^2/17)+(4.9^2/15))

t=0.86

There is insufficient evidence to suggest that there is a difference in the mean IQ for seventh grade boys and girls at the school.