Question

2. Suppose a new standardized test is given to 100 randomly selected third-grade students in New Jersey. The sample average score, Y¯ , on the test is 58 points, and the sample standard deviation, sY , is 8 points. (a) Construct a 95% confidence interval for the mean score of all New Jersey third graders.

(b) Suppose the same test is given to 200 randomly selected third graders in Iowa, producing a sample average of 62 points and a sample standard deviation of 11 points. Derive the formula for the sample variance of the difference in the sample means between New Jersey and Iowa.

(c) Construct a 90% confidence interval for the difference in mean scores between Iowa and New Jersey. Can you conclude that the population means for Iowa and New Jersey students are different?

Answer #1

Grades on a standardized test are known to have a mean of
10901090
for students in the United States. The test is administered
to
458458
randomly selected students in Florida; in this sample, the
mean is
1104.171104.17
and the standard deviation
(s)
is
117.72117.72.
The 95% confidence interval for the average test score for
Florida students is
(nothing,
nothing).
(Round
your responses to two decimal
places.)

A sample of 14 randomly selected students have a sample mean
score of 27.6 with a sample standard deviation of 5.1 on a
placement test. Construct a 95% confidence interval for the mean
score, !, of all students taking the test.

A random sample of 36 seventh grade students in Harvard are
given a test on a reading test. Below are their raw scores.
73, 77, 80, 80, 84, 86, 91, 93, 93, 93, 94, 97, 100, 100, 103,
103, 104, 105, 105, 106, 108, 110, 111, 117. 120, 120, 123, 124,
126, 128, 129, 129, 130, 130, 136
Sample mean = 105.97
Sample standard deviation = 17.18
Nationally 30% of the students score 110 points or higher on
this test....

16 students were randomly selected from a large group of
students taking a certain calculus test. The mean score for the
students in the sample was 86 and the standard deviation was 1.3.
Assume that the scores are normally distributed. Construct a 98%
confidence interval for the mean score, μ, of all students taking
the test. Round your answer to two decimal places.

A simple random sample of 23 third-grade children from a certain
school district is selected, and each is given a test to measure
his/her reading ability. You are interested in calculating a 90%
confidence interval for the population mean score. In the sample,
the mean score is 64 points and the standard deviation is 14
points. What is the margin of error associated with the confidence
interval?

The State Department of Education is developing a new test to
measure the reading
level of sixth graders. To pilot this test, they select a random
sample of 50 sixth
graders from within the state and have them take the test. The mean
score for the
students in this sample is 70.5 points. Suppose that it is already
known that the
standard deviation for all sixth graders in the state is 8.4
points.
A.Construct and interpret a 98% confidence interval...

A sample of 25 randomly selected students has a mean test score
of 81.5 with a standard deviation of 10.2. Assuming that the
population has a normal distribution, use this sample data to
construct a 95% confidence interval for the population mean μ of
all test scores.
A. (77.29, 85.71)
B. (56.12, 78.34)
C. (87.12, 98.32)
D. (66.35, 69.89)

16 students were randomly selected from a large group of
students taking a certain calculus test. The mean score for the
students in the sample was 86 and the standard deviation was 1.2.
Assume that the scores are normally distributed. Construct a 98%
confidence interval for the mean score, μ, of all students taking
the test. Round your answer to two decimal places.
a- (85.30 , 86.70)
b- (85.22 , 86.78)
c- (85.36 , 86.64)
d- (85.28 , 86.72)

5) Suppose that simple random samples of college freshman are
selected from two universities, 25 students from school A and 20
students from school B. On a standardized test, the sample from
school A has an average score of 1010 with a standard deviation of
100. The sample from school B has an average score of 990 with a
standard deviation of 90.
a) What is the 90% confidence interval for the difference in
test scores at the two schools?...

A group of 51 randomly selected students have a mean score of
29.5 with a sample standard deviation of 5.2 on a placement test.
What is the 95% confidence interval for the
mean score, μ, of all students taking the test?
Critical error=
Margin of error=
confidence interval=

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