Question

If the quality of teaching is similar in a school, the scores on a standardized test...

If the quality of teaching is similar in a school, the scores on a standardized test will have a standard deviation of 27 . The superintendent wants to know if there is a disparity in teaching quality, and decides to investigate whether the standard deviation of test scores has changed. She samples 25 random students and finds a mean score of 161 with a standard deviation of 13.2914 . Is there evidence that the standard deviation of test scores has decreased at the α = 0.01 level?

Assume the population is normally distributed. Step 2 of 5 : Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places.

Homework Answers

Answer #1

Let be the population standard deviation .

We want to test whether is changed from 27

So our Hypotheses are

Ho : = 27 vs Ha :

From sample, sample size n= 25

Sample standard deviation s = 13.2914

Test statictic is

= 5.816

Here alpha = 0.01 and df for chi square distribution is n-1 = 24

This is two tailed test . From chi square table

Upper critical value = 45.558

Lower critical value = 9.886

We will Reject Ho if test statistic is less than 9.886 or more than 45.558

Here test statistic is less than 9.886

So reject Ho

There is enough evidence that standard deviation has changed and also standard deviation has decreased.

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
If the quality of teaching is similar in a school, the scores on a standardized test...
If the quality of teaching is similar in a school, the scores on a standardized test will have a standard deviation of 1616. The superintendent wants to know if there is a disparity in teaching quality, and decides to investigate whether the standard deviation of test scores has changed. She samples 2626 random students and finds a mean score of 166166 with a standard deviation of 17.982217.9822. Is there evidence that the standard deviation of test scores has increased at...
If the quality of teaching is similar in a school, the scores on a standardized test...
If the quality of teaching is similar in a school, the scores on a standardized test will have a standard deviation of 19. The superintendent wants to know if there is a disparity in teaching quality, and decides to investigate whether the standard deviation of test scores has changed. She samples 22 random students and finds a mean score of 110 with a standard deviation of 16.709. Is there evidence that the standard deviation of test scores has decreased at...
PLEASE DOUBLE CHECK ANSWER IS CORRECT & DON'T USE HANDWRITTEN ANSWERS. THANK YOU! If the quality...
PLEASE DOUBLE CHECK ANSWER IS CORRECT & DON'T USE HANDWRITTEN ANSWERS. THANK YOU! If the quality of teaching is similar in a school, the scores on a standardized test will have a standard deviation of 16. The superintendent wants to know if there is a disparity in teaching quality, and decides to investigate whether the standard deviation of test scores has changed. She samples 26 random students and finds a mean score of 186 with a standard deviation of 7.276....
In a school district, all sixth grade students take the same standardized test. The superintendant of...
In a school district, all sixth grade students take the same standardized test. The superintendant of the school district takes a random sample of 26 scores from all of the students who took the test. She sees that the mean score is 121 with a standard deviation of 14.3688. The superintendant wants to know if the standard deviation has changed this year. Previously, the population standard deviation was 24. Is there evidence that the standard deviation of test scores has...
The quality of the elementary school teachings is very important, and the effectiveness of teaching can...
The quality of the elementary school teachings is very important, and the effectiveness of teaching can be shown by the students’ performance on the standardized test. The state requires that the average score of the 5th grade students from each school need to be at least 75. If any school’s average score is below 75, the school will be investigated further to ensure their quality of teaching. For School A, 20 5th grade students are randomly selected to take the...
A random sample of 64 second-graders in a certain school district are given a standardized mathematics...
A random sample of 64 second-graders in a certain school district are given a standardized mathematics skills test. The sample mean score is 51.21. Assume the standard deviation for the population of test scores is 15. The nationwide average score on this test is 50. The school superintendent wants to know whether the second-graders in her school district have greater math skills than the nationwide average. Perform the hypothesis test and compute the p-value. Round to four decimal places.
A standardized​ exam's scores are normally distributed. In a recent​ year, the mean test score was...
A standardized​ exam's scores are normally distributed. In a recent​ year, the mean test score was 1468 and the standard deviation was 314. The test scores of four students selected at random are 1890​, 1220​, 2180​, and 1360. Find the​ z-scores that correspond to each value and determine whether any of the values are unusual. The​ z-score for 1890 is __. ​ The​ z-score for 1220 is __. The​ z-score for 2180 is __. The​ z-score for 1360 is __....
A principal claims the students in his school have above-average test scores for a particular standardized...
A principal claims the students in his school have above-average test scores for a particular standardized test. A sample of 50 students from his school were found to have an average test score of 77.2. The population mean for test scores for this particular test is 75, with a standard deviation of 9 (so we can assume that the population test score is normally distributed). Set up a hypothesis test to determine whether this principal’s claim is correct (use alpha...
In a recent​ year, scores on a standardized test for high school students with a 3.50...
In a recent​ year, scores on a standardized test for high school students with a 3.50 to 4.00 grade point average were normally​ distributed, with a mean of 38.238.2 and a standard deviation of 2.22.2. A student with a 3.50 to 4.00 grade point average who took the standardized test is randomly selected. ​(a) Find the probability that the​ student's test score is less than 3737. The probability of a student scoring less than 3737 is 0.29120.2912. ​(Round to four...
A random sample of 12 high school seniors took a standardized mathematics test and made scores:...
A random sample of 12 high school seniors took a standardized mathematics test and made scores: 78, 78, 65, 77, 65, 81, 83, 59, 76, 75, 83, 59 Past scores at the same high school have been Normally distributed with LaTeX: \sigma σ =9.3 Is this sample evidence at the α =0.01 level that the average test score for all students is less than 75? State the hypotheses and calculate a test statistic and P-value in order to answer the...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT