Question

• Math SAT scores (Y ) are normally distributed with a mean of 500 and a standard deviation

of 100. An evening school advertises that it can improve students’ scores by roughly a

third of a standard deviation, or 30 points, if they attend a course which runs over several

weeks. The statistician for a consumer protection agency suspects that the courses are

not effective. She views the situation as follows: H0 : E(Y ) = 500 vs. H1 : E(Y ) = 530.

The consumer protection agency wants to evaluate this claim by sending 50 students to

attend classes. One of the students becomes sick during the course and drops out.

(Q4) What is the distribution of the average score of the remaining 49 students under the null,

and under the alternative hypothesis?

(Q5) Compute the power of the test.

(Q6) What options does the statistician have for increasing the power in this situation without

changing its size?

Answer #1

Q6: Increase the sample size for increasing the power without changing the size of the test.

Suppose the mathematics SAT scores are normally distributed
with a mean of 500 and a standard deviation of 100. If a school
only accepts students with SAT math scores in the top 10 percent,
what are the minimum SAT scores that would be acceptable for that
school?

For all U.S. students nationally who take the SAT, SAT Math
scores are normally distributed with an average score of 500 for
all U.S. students and a population standard deviation of 125. A
random sample of 100 students entering Whitmer College had an
average SAT Math (SAT-M) score of 530.
The sample data can be used to test the claim that
the mean SAT-M score of all Whitmer College students is different
than the national mean SAT-M score.
From the...

The SAT scores earned on the math portion are approximately
normally distributed with mean 516 and standard deviation 116.
Answer the following questions based on this information. Make sure
you show your work.
1. Using a printout of the graph above or making your own copy,
mark the mean SAT score on the math proportion at the appropriate
place. Then mark values of score that are 1, 2, and 3 standard
deviations away from the mean value. Labeling your marks...

Combined math and verbal SAT scores are normally distributed with a
mean of 1010 and a standard deviation of 190. Elite University's
admissions office requires a comined SAT score in the top 20% of
all students taking the test. What is their cutoff score for
admission?

The scores on the SAT college entrance exam are normally
distributed with a mean Math score of 480 and a standard deviation
of 100. If you select 50 students, what is the probability that
their mean Math score is more than 520. You MUST show what went
into the calculator along with your final answer rounded correctly
to 3 significant decimal places.

For all U.S. students nationally who take the SAT, SAT Math
scores are normally distributed with an average score of 500 for
all U.S. students . A random sample of 100 students entering
Whitmer College had an average SAT Math (SAT-M) score of 475 and a
sample standard deviation of 120. The sample data can be used to
test the claim that the mean SAT-M score of all Whitmer College
students is lower than the national mean SAT-M score. Based...

For all U.S. students nationally who take the SAT, SAT Math
scores are normally distributed with an average score of 500 for
all U.S. students . A random sample of 100 students entering
Whitmer College had an average SAT Math (SAT-M) score of 520 and a
sample standard deviation of 120. The sample data can be used to
test the claim that the mean SAT-M score of all Whitmer College
students is higher than the national mean SAT-M score. Based...

A national placement test has scores that are normally
distributed with a mean of 500 and a standard deviation of 100.
a) A certain college requires a
minimum score of 600. What percent of students would meet that
criteria?
b) A different college will accept only the top 10%. What is the
college’s cutoff score?

Q1-. A normal distribution has a mean of 15 and a standard
deviation of 2. Find the value that corresponds to the 75th
percentile. Round your answer to two decimal places.
Q2-.Tyrell's SAT math score was in the 64th percentile. If all
SAT math scores are normally distributed with a mean of 500 and a
standard deviation of 100, what is Tyrell's math score? Round your
answer to the nearest whole number.
Q3-.Find the z-score that cuts off an area...

Q1-. A normal distribution has a mean of 15 and a standard
deviation of 2. Find the value that corresponds to the 75th
percentile. Round your answer to two decimal places.
Q2-.Tyrell's SAT math score was in the 64th percentile. If all
SAT math scores are normally distributed with a mean of 500 and a
standard deviation of 100, what is Tyrell's math score? Round your
answer to the nearest whole number.
Q3-.Find the z-score that cuts off an area...

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