Question

A high school principle currently encourages students to enroll in a specific SAT prep program that has a reputation of improving score by 50 points on average. A new SAT prep program has been released and claims to be better than their current program. The principle is thinking of advertising this new program to students if there is enough evidence at the 5% level that their claim is true. The principle tests the following hypotheses:

H0:μ=50 points

HA:μ>50 points

where μμ is the true mean in difference of scores after the new SAT prep course is taken and before the new SAT prep course is taken. He randomly assigns 93 students to take this new SAT program. The difference in scores resulted in an average of 50.3364 points with a standard deviation of 13.0174 points.

**What is the value of the test statistic for this test?
Round your answer to four decimal places.**

**What is your decision regarding the null
hypothesis?**

A. Reject the null hypothesis, at the 5% significance level, there is not enough evidence to say that the new SAT prep program is better than the current SAT prep program.

B. Fail to reject the null hypothesis, at the 5% significance level, there is not enough evidence to say that the new SAT prep program is better than the current SAT prep program.

C. Fail to reject the null hypothesis, at the 5% significance level, there is enough evidence to say that the new SAT prep program is better than the current SAT prep program.

D. Reject the null hypothesis, at the 5% significance level, there is enough evidence to say that the new SAT prep program is better than the current SAT prep program.

The average height of men in 1960 was found to be 68 inches (5 feet, 8 inches). A researcher claims that men today are taller than they were in 1960 and would like to test this hypothesis at the 0.01 significance level. The researcher randomly selects 184 men and records their height to find an average of 69.7020 inches with standard deviation of 1.1125 inches.

**What is the value of the test statistic? Round your
answer to four decimal places.**

**What is your decision regarding the null
hypothesis?**

A. Fail to reject the null hypothesis. At the 1% significance level there is not sufficient evidence to say that men today are taller than they were in 1960.

B. Fail to reject the null hypothesis. At the 1% significance level there is sufficient evidence to say that men today are taller than they were in 1960.

C. Reject the null hypothesis. At the 1% significance level there is not sufficient evidence to say that men today are taller than they were in 1960.

D. Reject the null hypothesis. At the 1% significance level there is sufficient evidence to say that men today are taller than they were in 1960.

Answer #1

Ans:

1)

Test statistic:

z=(50.3364-50)/(13.0174/SQRT(93))

z=0.2492

Option B is correct.

Fail to reject the null hypothesis, at the 5% significance level, there is not enough evidence to say that the new SAT prep program is better than the current SAT prep program.

2)

Test statistic:

z=(69.702-68)/(1.1125/SQRT(184))

z=20.7524

Option D is correct.

Reject the null hypothesis. At the 1% significance level there is sufficient evidence to say that men today are taller than they were in 1960.

Determine the critical value(s) of the test statistic for each
of the following small sample tests for the population mean where
the assumption of normality is satisfied. Round your answer to four
decimal places.
Left-tailed test,α=0.01,n=24
Right-tailed test ,α=0.1,n=8
Two-tailed test, α=0.05,n=12
A high school principle currently encourages students to enroll
in a specific SAT prep program that has a reputation of improving
score by 50 points on average. A new SAT prep program has been
released and claims to...

A high school principle currently encourages students to enroll
in a specific SAT prep program that has a reputation of improving
score by 50 points on average. A new SAT prep program has been
released and claims to be better than their current program. The
principle is thinking of advertising this new program to students
if there is enough evidence at the 5% level that their claim is
true. The principle tests the following hypotheses:
H0:μ=50 points HA:μ>50 points
where...

The average height of men in 1960 was found to be 68 inches (5
feet, 8 inches). A researcher claims that men today are taller than
they were in 1960 and would like to test this hypothesis at the
0.01 significance level. The researcher randomly selects 9797 men
and records their height to find an average of 69.702069.7020
inches with standard deviation of 2.0024 inches.
Step 1 of 2:
What is the value of the test statistic? Round your answer...

SmArT Academy, an SAT test prep company, claims that their
program improves student scores). A simple random sample of 37
students took the SAT before taking the prep course and then again
after taking the prep course. The average increase in their scores
after taking the course was 40 points with a standard deviation of
120 points. What can we conclude about the SmArT Academy’s claim
that the course improves scores? Use a significance level of α =
0.05 and...

An SAT prep course claims to improve the test score of students.
The table below shows the scores for seven students the first two
times they took the verbal SAT. Before taking the SAT for the
second time, each student took a course to try to improve his or
her verbal SAT scores. Do these results support the claim that the
SAT prep course improves the students' verbal SAT scores? Let
d=(verbal SAT scores prior to taking the prep course)−(verbal...

An SAT prep course claims to improve the test score of students.
The table below shows the scores for seven students the first two
times they took the verbal SAT. Before taking the SAT for the
second time, each student took a course to try to improve his or
her verbal SAT scores. Do these results support the claim that the
SAT prep course improves the students' verbal SAT scores?
Let d=(verbal SAT scores prior to taking the prep
course)−(verbal...

SmArT Academy, an SAT test prep company, claims that their
program improves student scores). A simple random sample of 37
students took the SAT before taking the prep course and then again
after taking the prep course. The average increase in their scores
after taking the course was 40 points with a standard deviation of
120 points. What can we conclude about the SmArT Academy’s claim
that the course improves scores? Use a significance level of α =
0.05 and...

An educator randomly assigns students to a program in which some
will use new reading activities and others traditional teaching
methods. At the end, both groups take a reading comprehension
exam. Their scores are shown in the back-to-back stem-and-leaf
display. Do these results suggest that the new activities are
better? Test an appropriate hypothesis and state your
conclusion.
(Assume a significance level of α=0.05.)
Compute the t-statistic. t = ___________
(Round to three decimal places as needed.)
Find the P-value....

Retaking the SAT: Many high school students
take the SAT's twice; once in their Junior year and once in their
Senior year. In a sample of 55 such students, the score on the
second try was, on average, 34 points above the first try with a
standard deviation of 15 points. Test the claim that retaking the
SAT increases the score on average by more than 30 points. Test
this claim at the 0.10 significance level.
(a) The claim is...

Retaking the SAT: Many high school students
take the SAT's twice; once in their Junior year and once in their
Senior year. In a sample of 55 such students, the score on the
second try was, on average, 33 points above the first try with a
standard deviation of 14 points. Test the claim that retaking the
SAT increases the score on average by more than 30 points. Test
this claim at the 0.01 significance level.
(a) The claim is...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 6 minutes ago

asked 10 minutes ago

asked 10 minutes ago

asked 24 minutes ago

asked 25 minutes ago

asked 32 minutes ago

asked 35 minutes ago

asked 43 minutes ago

asked 44 minutes ago

asked 52 minutes ago

asked 52 minutes ago

asked 52 minutes ago