Question

For the general population, IQ test scores are normally distributed with a mean of 100 and a variance of 225.

The IQ scores for a sample of 81 randomly selected chemical engineers resulted in a variance of 144.

We want to test the claim that the variance for chemical engineers is less than that of the general population.

1. What is the Null Hypothesis and the Alternative Hypothesis?

2. If we use a 0.01 significance level, what is the critical value for the test?

3. What is the value of the test statistic?

4. What is your decision about the null hypothesis? What is your conclusion about the claim?

Answer #1

IQ scores among the general population have a mean of
100
and a standard deviation of
15
. A researcher claims that the standard deviation,
σ
, of IQ scores for males is less than
15
. A random sample of
16
IQ scores for males had a mean of
98
and a standard deviation of
10
. Assuming that IQ scores for males are approximately normally
distributed, is there significant evidence (at the
0.1
level of significance) to conclude...

In the population, IQ scores are normally distributed with a
mean of 100. A charter school wants to know if their students have
an IQ that is higher than the population mean. They take a random
sample of 15 students and find that they have a mean IQ of 109 with
a sample standard deviation of 20. Test at 1% significance level
whether the average IQ score in this school is higher than the
population mean.
a) Write down null...

In the general population, IQ scores are approximately normally
distributed with a mean of 100 and a standard deviation of 15.
Lewis Terman developed the idea of IQ and proposed classifying
people with IQ scores over 140 as "genius".
1. What percent of the general population have IQ scores that
would be classified as genius?
2. Give a range of values that would include IQ scores for the
middle 75% of the general population.

You wish to test the
claim that the average IQ score is less than 100 at the .005
significance level. You determine the hypotheses are:
Ho: μ=100
H1:μ<100
You take a simple
random sample of 76 individuals and find the mean IQ score is 95.5,
with a standard deviation of 15.1. Let's consider testing this
hypothesis two ways: once with assuming the population standard
deviation is not known and once with assuming that it is known.
Round to three decimal...

You wish to test the claim that the average IQ score is less
than 100 at the .01 significance level. You determine the
hypotheses are: H o : μ = 100 H 1 : μ < 100 You take a simple
random sample of 60 individuals and find the mean IQ score is 98.7,
with a standard deviation of 14.6. Let's consider testing this
hypothesis two ways: once with assuming the population standard
deviation is not known and once with...

You wish to test the claim that the average IQ score is less
than 100 at the .005 significance level. You determine the
hypotheses are: H o : μ = 100 H 1 : μ < 100 You take a simple
random sample of 95 individuals and find the mean IQ score is 95.2,
with a standard deviation of 14.4. Let's consider testing this
hypothesis two ways: once with assuming the population standard
deviation is not known and once with...

A certain IQ test is known to have a population mean of 100 and
standard deviation of 15 in the general population. You want to
test whether psychology majors have a different average IQ than the
population as a whole. Assume the variance of IQ is the same for
Psych majors as it is in the general population.
Suppose that Psychology majors actually have an average IQ of
108. If you do a 2-tailed test at α= .05 with a...

The Stanford-Binet IQ test has scores that are normally
distributed with a mean of 100. A principal in an elementary school
believes that her students have above average intelligence and
wants verification of her belief. She randomly selects 20 students
and checks the student files. She finds the following IQ scores for
these 20 students. IQ scores: 110,132, 98, 97, 115, 145, 77, 130,
114, 128, 89, 101, 92, 85, 112, 79, 139, 102, 103, 89
a. Compute the sample...

7. In the general population, IQ scores have a mean of 100, a
standard deviation of 15, and a normal distribution. a. If a person
is randomly selected from the general population, what is the
probability of getting a person with an IQ below 122? (Show as much
work as possible. You can leave your answer with all 4 decimal
places) b. What percentage of the general population has an IQ
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Scores on IQ test are normally distributed. A sample
of 14 IQ scores had standard deviation s=6. Construct a 99%
confidence interval for the population standard deviation. The
developerof the test claims that the population standard deviation
is =7. Does this confidence interval contradict this claim?

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