Question

a sample have 10 students the average score in math is less than the average in...

a sample have 10 students
the average score in math is less than the average in english
x1= test scores in math
x2= test scores in english
assume the scores follow normal distribution

let u1 be the population mean of math scored
let u2 be the population mean of english score
the score are given below
student. math. english
1. 18. 22
2. 22. 24
3. 19. 16
4. 23. 19
5. 20. 21
6. 18. 18
7. 16. 17
8. 17. 20
9. 21. 25.
10. 14. 15

A: are the observation independent?
B construct a 95% CI for the mean difference
C: test the hypothesis that whether the average score on math is less than average score in english at 5% level

Homework Answers

Answer #1

A. No, the observation are not independent, as the samples are dependent.

B.

Student Math English Difference
1 18 22 4
2 22 24 2
3 19 16 -3
4 23 19 -4
5 20 21 1
6 18 18 0
7 16 17 1
8 17 20 3
9 21 25 4
10 14 15 1
Average 1.8
Std.Dev. 1.6432

Here paired size n = 10

degree of freedom = 10 - 1

95% CI for mean difference = dbar +- tcritical sed

= 1.8 +- 2.26216 * 1.6432/sqrt(10)

= 1.8 +- 1.1755

=(0.6245, 2.9755)

(C) Here as the confidence interval doesn't consist the value of 0 so we can conclude that  the average score on math is less than average score in english at 5% level.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
(i) Suppose for a sample of 12 students, the average scores in Math and English are...
(i) Suppose for a sample of 12 students, the average scores in Math and English are 85 and 73 respectively, and the regression equation relating the Math scores (x) to English scores (y) is given by:  y′=0.7+0.85x. Assuming that there is a significant linear correlation between the Math and English scores, predict the English score of a student who scored 91 in Math. Round your answer to the nearest whole number. (ii) What would the answer in part (i) be if...
Test, at the 1% level of significance, whether the average business has more than 15 employees....
Test, at the 1% level of significance, whether the average business has more than 15 employees. Answer using excel. Employees 14 17 17 6 8 17 21 16 6 17 11 17 15 16 20 19 6 12 17 22 20 17 11 11 9 22 17 18 21 20 26 7 16 19 18 11 21 17 25 16 22 14 14 16 18 20 21 11 19 13 6 11 19 14 18 31 13 15 17 21...
A study was conducted to see if students’ writing skills continue to improve as the academic...
A study was conducted to see if students’ writing skills continue to improve as the academic year progresses. English 101 students were asked to write essays throughout the year in September, December, March and June. The scores were compared to see if there is any improvement in this one-year course. Was there a significant improvement? The appropriate test for this problem is: one-way ANOVA repeated measurements Student September December March June 1 17 23 21 24 2 25 21 21...
For all U.S. students nationally who take the SAT, the average SAT Math score is 500,...
For all U.S. students nationally who take the SAT, the average SAT Math score is 500, with a population standard deviation of 125. A random sample of 10 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. Based on the given information, have the conditions for this hypothesis...
Do students tend to improve their SAT math score the second time they take the test?...
Do students tend to improve their SAT math score the second time they take the test? A random sample of four students who took the test twice provided the given scores. Student 1 2 3 4 First Score 450 520 720 600 Second Score 440 600 720 630 Assuming that the change in SAT Math score (second score—first score) for the population of all students taking the test twice is Normally distributed with mean μ , are we convinced that...
2. A sample of ACT scores for 20 students in Basic Math revealed a mean score...
2. A sample of ACT scores for 20 students in Basic Math revealed a mean score of 10 with a standard deviation of 3. Find a 96 percent confidence interval for the mean ACT score for all basic math students.
Two sample Dependent t-test (or Paired t-test) You want to test your hypothesis below: There is...
Two sample Dependent t-test (or Paired t-test) You want to test your hypothesis below: There is a difference in mean test scores between Exam 1 and Exam 2             Provide your answers in the template below the data set. Exam 1 Exam 2 17 19 18 20 16 22 18 24 12 10 20 25 18 20 20 22 20 21 22 23 20 20 10 10 8 12 12 14 16 12 16 20 18 22 20 24 18...
Statistics students in Quebec Universities score 75.91 on average on a test of basic math ability....
Statistics students in Quebec Universities score 75.91 on average on a test of basic math ability. The standard deviation of the test scores is 14.1415. If we choose 8 students at random and give them the test, what is the exact probability that the mean of these 8 scores will be 70.00 or lower?
Eleanor scores 680 on the math portion of the SAT. The distribution of math SAT scores...
Eleanor scores 680 on the math portion of the SAT. The distribution of math SAT scores is approximately Normal, with mean 500 and standard deviation 100. Jacob takes the ACT math test and scores 27. ACT math test scores are Normally distributed with mean 18 and standard deviation 6. a. Find the standardized scores (z-scores) for both students. b. Assuming that both tests measure the same kind of ability, who has the higher score? c. What score must a student...
A city officials claim that average transit usage in the city is less than 20%. Based...
A city officials claim that average transit usage in the city is less than 20%. Based on previous studies in different parts of the city, it is known that the share of transit is normally distributed in the city with a standard deviation of 3.5. A research group collected data for different parts of the city and ended up with 12 observations for transit usage in different parts of the city: 20, 18, 19, 16, 18, 26, 22, 19, 24,...