In: Statistics and Probability

1. Nine students took the SAT test. Their scores are listed below. Later on, they took a test preparation course and retook the SAT. Their new scores are listed below. Use the Sign test to test the claim that the test preparation has no effect on their scores. Use α = 0.05.

Student |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |

Before |
860 |
820 |
910 |
990 |
1000 |
930 |
870 |
1180 |
920 |

After |
880 |
820 |
900 |
1030 |
1030 |
940 |
860 |
1220 |
940 |

2. A medical researcher wishes to try three different techniques to lower blood pressure of patients with high blood pressure. The subjects are randomly selected and randomly assigned to one of three groups. Group 1 is given medication, Group 2 is given an exercise program, and Group 3 is assigned a special diet. At the end of six weeks, the reduction in each subject's blood pressure is recorded. Use the Kruskal-Wallis test to test the claim that there is no difference in the distributions of the blood pressures of the three populations. Use α = 0.05.

Group 1 |
Group 2 |
Group 3 |

13 |
10 |
8 |

Nine students took the SAT. After taking it, they then took a
test preparation course and retook the SAT. Can you conclude that
the course changes performance on the SAT? (use α = .1)

nn psychology students took a standardized test. The scores are
summarized in the GFDT below.
Scores
Frequency
220 - 224
14
225 - 229
15
230 - 234
16
235 - 239
240 - 244
17
245 - 249
40
The scores are also described in the cumulative table shown
below.
Scores
Frequency
less than 225
14
less than 230
29
less than 235
45
less than 240
63
less than 245
80
less than 250
nn
What is the...

1. The test scores of 10 students are listed below.
32, 69, 77, 82, 100, 68, 88, 95, 75, 80
a. Determine the five-number summary and draw a boxplot for the
given data above.
Minimum ________
Q1 ________
Median ________
Q3 ________
Maximum ________
b. Which number(s) is suspected outliers? Justify your answer.
c. Is it possible to have a mean of 96 if the scores ranged from 65
to 95? Justify your answer.

2. A sample of 32 students took a class designed to improve
their SAT math scores. Their scores before and after the class are
recorded in the sheet ‘SAT Scores’ in the ‘Lab12 Chp 10n11 S20’
spreadsheet.
(a) Are the samples independent or paired?
(b) Consider constructing a 90% confidence interval for the
average increase in scores after taking the class.
i. Find the point of estimate using proper notation. Show your work
including all relevant quantities needed. Round...

A certain test preparation course is designed to improve
students' SAT Math scores. The students who took the prep course
have a mean SAT Math score of 526, while the students who did not
take the prep course have a mean SAT Math score of 515. Assume that
the population standard deviation of the SAT Math scores for
students who took the prep course is 44.6 and for students who did
not take the prep course is 45.2. The SAT...

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...

The test scores of 10 students are listed below. 32, 69, 77, 82,
100, 68, 88, 95, 75, 80 a. Determine the five-number summary and
draw a boxplot for the given data above. Minimum ________ Q1
________ Median ________ Q3 ________ Maximum b. Is there any
outlier? Justify your answer. c. Which of the measures of center
would be best to represent the data? Justify your answer

A test prep website claims that students who use their service
improve their SAT scores by more than 109 points. After using the
site, a random sample of 25 students improved by an average of 102
points with a standard deviation of 23.2 points.

Continuing the discussion about SAT scores, these parameters are
for all people who took the SAT, not just students who went to
college. However, there are some assumptions that people with
higher SAT scores will make certain choices. One such choice is the
decision to go to college. We do not know the data (mean and
standard deviation) for students who go to college, but we can
estimate it with a sample. We took a random sample of 27 first...

Scores on the SAT Mathematics test are believed to be normally
distributed. The scores of a simple random sample of five students
who recently took the exam are 570, 620, 710, 540 and 480. We want
to find a 95% confidence interval of the population mean of SAT
math scores.
A) Calculate the point estimate. (Round to four decimal places
as needed.)
B) Calculate the sample standard deviation. (Round to four
decimal places as needed.)
C) Calculate the standard error...

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