In: Statistics and Probability

A fitness course claims that it can improve an individual's physical ability. To test the effect of a physical fitness course on one's physical ability, the number of sit-ups that a person could do in one minute, both before and after the course, was recorded. Ten individuals are randomly selected to participate in the course. The results are displayed in the following table. Can it be concluded, from the data, that participation in the physical fitness course resulted in significant improvement? Let d=(number of sit-ups that can be done after taking the course)−(number of sit-ups that can be done prior to taking the course) . Use a significance level of α=0.01 for the test. Assume that the numbers of sit-ups are normally distributed for the population both before and after taking the fitness course.

Sit-ups before | 20 | 38 | 24 | 26 | 38 | 55 | 23 | 42 | 44 | 44 |

Sit-ups After | 36 | 43 | 26 | 37 | 50 | 58 | 38 | 51 | 59 | 49 |

Step 1 of 5 : State the null and alternative hypotheses for the test.

Step 2 of 5: Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.

Step 3 of 5: Compute the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5: Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to three decimal places.

Step 5 of 5: Make the decision for the hypothesis test.

step 1 of 5 :

null Hypothesis: |
μ_{d} |
= | 0 | |

alternate Hypothesis: |
μ_{d} |
> | 0 |

Step 2 of 5: Find the value of the standard deviation of the paired differences Sd =5.3

Step 3 of 5: Compute the value of the test statistic =5.549 ( please try 5.579 if this comes wrong)

Step 4 of 5: Determine the decision rule:

Decision rule : reject Ho if test statistic t>2.821 |

Step 5 of 5: reject Ho

A fitness course claims that it can improve an individual's
physical ability. To test the effect of a physical fitness course
on one's physical ability, the number of sit-ups that a person
could do in one minute, both before and after the course, was
recorded. Ten individuals are randomly selected to participate in
the course. The results are displayed in the following table. Can
it be concluded, from the data, that participation in the physical
fitness course resulted in significant...

A fitness course claims that it can improve an individual's
physical ability. To test the effect of a physical fitness course
on one's physical ability, the number of sit-ups that a person
could do in one minute, both before and after the course, was
recorded. Ten individuals are randomly selected to participate in
the course. The results are displayed in the following table. Can
it be concluded, from the data, that participation in the physical
fitness course resulted in significant...

A fitness course claims that it can improve an individual's
physical ability. To test the effect of a physical fitness course
on one's physical ability, the number of sit-ups that a person
could do in one minute, both before and after the course, was
recorded. Ten individuals are randomly selected to participate in
the course. The results are displayed in the following table. Can
it be concluded, from the data, that participation in the physical
fitness course resulted in significant...

To test the effect of a physical fitness course on one's
physical ability, the number of sit-ups that a person could do in
one minute, both before and after the course, was recorded. Ten
individuals are randomly selected to participate in the course. The
results are displayed in the following table. Using this data, find
the 95% confidence interval for the true difference in the number
of sit-ups each person can do before and after the course. Assume
that the...

To test the effect of a physical fitness course on one's
physical ability, the number of sit-ups that a person could do in
one minute, both before and after the course, was recorded. Ten
individuals are randomly selected to participate in the course. The
results are displayed in the following table. Using this data, find
the 90% confidence interval for the true difference in the number
of sit-ups each person can do before and after the course. Assume
that the...

To test the effect of a physical fitness course on one's
physical ability, the number of sit-ups that a person could do in
one minute, both before and after the course, was recorded. Ten
individuals are randomly selected to participate in the course. The
results are displayed in the following table. Using this data, find
the 99%
confidence interval for the true difference in the number of
sit-ups each person can do before and after the course. Assume that
the...

To test the effect of a physical-fitness course on one’s
physical ability, the number of sit-ups that a person could do in 1
minute, both before and after the course, was recorded. Six
randomly selected participants scored as shown below. Can we
conclude that a significant amount of improvement took place? Use α
= 0.01 and assume normality. (Please show all steps of classical
approach.)
Before 29 22 25 29 26 24
After 30 26 25 35 33 36

An instructor for a test preparation course claims that the
course will improve the test scores of students. The table shows
the critical reading scores for 14 students the first two times
they took the test. Before taking the test for the second time,
the students took the instructor's course to try to improve their
critical reading test scores. At a = 0.01, is there enough
evidence to support the instructor's claim? Complete parts (a)
through (f). number of students:14....

24)____________ An SAT prep
course claims to improve the test scores of students. The
table
shows the scores for seven students the first two times they
took
25)_____________ 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.
Test the claim at a = .05. List the a) null
hypothesis b) average
difference
between
the scores
Student
1
2...

An SAT prep course claims to improve the test scores of
students. The table shows the critical reading scores for 10
students the first two times they took the SAT, once before for the
course, and once after the course. Test the company’s claim at α =
0.01. Extra columns provided for calculations.
Student Score
Before
Score After 1 308 400 2 456 524 3 352 409 4 433 491 5 306 348 6 471
583 7 422 451 8...

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