Question

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.

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.

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 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 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 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 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 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 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 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 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: 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

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 10 minutes ago

asked 11 minutes ago

asked 21 minutes ago

asked 22 minutes ago

asked 22 minutes ago

asked 29 minutes ago

asked 29 minutes ago

asked 29 minutes ago

asked 32 minutes ago

asked 36 minutes ago

asked 40 minutes ago