Question

In: Statistics and Probability

A group of 10 students who wish to enter a university achieve the following scores: 25,...

A group of 10 students who wish to enter a university achieve the following scores:

25, 17 , 29 , 29, 26, 24 , 23 , 26 , 24 , 33

...Construct a confidence interval for the proportion of students scoring 26 points or less.

...construct a 90% confidence interval for the average score of all students

Solutions

Expert Solution

using excel>Addin>phstat>confidence interval

we have

Confidence Interval Estimate for the Proportion
Data
Sample Size 10
Number of Successes 6
Confidence Level 90%
Intermediate Calculations
Sample Proportion 0.6
Z Value -1.64485363
Standard Error of the Proportion 0.154919334
Interval Half Width 0.254819628
Confidence Interval
Interval Lower Limit 0.345180372
Interval Upper Limit 0.854819628

a 90 % confidence interval for the proportion of students scoring 26 points or less is ( 0.3452 ,0.8548)

using excel>addin>phstat>confidence interval

we have

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation 14.37590577
Sample Mean 31
Sample Size 10
Confidence Level 90%
Intermediate Calculations
Standard Error of the Mean 4.546060566
Degrees of Freedom 9
t Value 1.833112933
Interval Half Width 8.333442416
Confidence Interval
Interval Lower Limit 22.67
Interval Upper Limit 39.33

a 90% confidence interval for the average score of all students (22.67,39.33)


Related Solutions

the following are the scores of 25 students who participated in a psychology experiment. The scores...
the following are the scores of 25 students who participated in a psychology experiment. The scores represent the number of trials required to complete a memorization test. 12, 10, 12, 11, 6, 15, 14, 17, 9, 12, 13, 8, 7, 15, 14, 15, 18, 19, 14, 10, 14, 14, 16, 8, 9 Based on these data, the z score for generated for a person with a raw score of 6 is___ and their percentile is___
If the scores of a group of students who are high in academic achievement (10 individuals)...
If the scores of a group of students who are high in academic achievement (10 individuals) on the academic self-   efficacy scale are as follows: 120-122-117-102-125-120-108-111-110-115 The scores of a group of students with low academic achievement (12 individuals) on the academic self-effectiveness scale are as follows: 72-69-72-75-77-80-68-75-77-87-70-85 Using spss, how to test the following hypothesis: There are no statistically significant differences between the mean scores of the sample individuals on the academic self-efficacy scale due to the difference in...
A university found that 10% of students withdraw from a math course. Assume 25 students are...
A university found that 10% of students withdraw from a math course. Assume 25 students are enrolled. Write the prob. distribution function with the specific parameters for this problem Compute by hand (can use calculator but show some work) the pro that exactly 2 withdraw. Compute by hand (can use calculator but show some work) the prob. that exactly 5 withdraw. Construct the probability distribution table of class withdrawals in Excel. This is a table of x and f(x). Generate...
The table below shows the scores of a group of students on a 10-point quiz. Test...
The table below shows the scores of a group of students on a 10-point quiz. Test ScoreFrequency 3 4 4 3 5 3 6 2 7 1 8 1 9 1 10 6 The mean score on this test is: The median score on this test is
A group of students takes a 10 point quiz. You have the scores for each student...
A group of students takes a 10 point quiz. You have the scores for each student and decide to calculate the correlation between (a) the number of correct answers on the quiz with (b) the number of incorrect answers on the quiz. A. What would r equal? If you’re stuck, think about this a bit. If you’re really stuck, it may help to make a scatterplot based 10 students getting various scores on the quiz. _________________ (1 point) B. How...
A university administrator expects that 25% of students in a core course will receive an A....
A university administrator expects that 25% of students in a core course will receive an A. He looks at the grades assigned to 60 students. a. What are the expected value and the standard error for the proportion of students that receive an A? b. Use an appropriate normal transformation to calculate the probability that the percentage of students that receive an A is 20% or less. c. Use an appropriate normal transformation to calculate the probability that the proportion...
A group of 20 students contains 10 who believe Anna is doing a good job, 5...
A group of 20 students contains 10 who believe Anna is doing a good job, 5 who believe Anna is doing a bad job and 5 who do not know who Anna is. Two students are chosen at random. What are the probabilities? Both do not know who Anna is One believes Anna is doing a good job and 1 who believes Trump is doing a poor job
A random sample of the ACT scores of 300 students at Big State University provided a...
A random sample of the ACT scores of 300 students at Big State University provided a sample mean score of 21.8 with a sample standard deviation of 5.632. Find the 95% confidence interval for the mean score of all Big State students who had taken the ACT.? (a) (21.2, 22.4) (b) (21.0, 22.6) (c) (20.9, 22.7) (d) (20.3, 23.3) (e) (21.3, 22.3)
  You wish to see the average improvement on SOL scores after students have completed a program....
  You wish to see the average improvement on SOL scores after students have completed a program. A random sample of 300 students who completed the program showed an average improvement of 4.35 points with a standard deviation of 0.96 points. Calculate and interpret a 90% confidence interval for the average improvement for all students who would complete this program. A: Verify the assumptions. B: Calculate a 90% confidence interval for the average improvement for all students who would complete this...
A group of 1000 students wrote an entrance exam for the University of Statistics. The mean...
A group of 1000 students wrote an entrance exam for the University of Statistics. The mean score was 62 with a standard deviation of 12. Assuming a Normal Distribution, answer the following questions: What is the probability of a student scoring above 75? What is the probability of a student failing? (i.e. below 50) How many students failed? What is the minimum mark you would need to score to be in the top 10%? What is the minimum mark you...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT