Question

Pretend you are a researcher interested in evaluating the IQ of a class of “gifted” fifth-graders to see whether their mean IQ is significantly higher than the mean IQ of the general population. You administer a standardized IQ test to the “gifted” fifth-grade class and the data are provided in “Raw Data.txt”. Assume it is known that the IQ test you are using has a mean of 100 and a standard deviation of 15 when given to fifth-graders in general. It is also known that the test scores of fifth-graders, in general, are normally distributed.

This is the Raw Data Set:

Students	IQ Score
1	109
2	116
3	115
4	103
5	115
6	106
7	102
8	112
9	118
10	119
11	117
12	120
13	113
14	118
15	120
16	121
17	119
18	116
19	118
20	110
21	100
22	103
23	107
24	112
25	111
26	108
27	100
28	100
29	102
30	118

I need to find:

Population Mean: 100 (which is already given in the hypothetical scenario)

Population Variance: (I need to find this one using the SD of 15, which was given in the hypothetical scenario)

Sample Mean:

Sample Size:

Answer 1

Let be the mean IQ of a class of “gifted” fifth-graders

To test whethermean IQ of “gifted” fifth-graders is significantly higher than the mean IQ of the general population which is given as 100 with SD 15

It is to test

Population mean =100, population SD =15 . Also given test scores are normally distributed

For testing a sample “gifted” fifth-graders of size, n = 30 is taken and their IQs are listed as follows in second column.

1	109
2	116
3	115
4	103
5	115
6	106
7	102
8	112
9	118
10	119
11	117
12	120
13	113
14	118
15	120
16	121
17	119
18	116
19	118
20	110
21	100
22	103
23	107
24	112
25	111
26	108
27	100
28	100
29	102
30	118

The sample mean is (sum of these 30 IQs)/30 =

Test statistics whcih following std normal distribution,

here is the value of under null hypothesis, which is 100.

From std normal table, at 5% level of significance, = 1.645

The calculated value of test statistic z is greater than the table value 1.645. Hence it is to reject null hypothesis and conclude that the mean IQ of “gifted” fifth-graders is significantly higher than the mean IQ of the general population.