1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
andrew-mc [135]
3 years ago
8

A professor would like to test the hypothesis that the average number of minutes that a student needs to complete a statistics e

xam has a standard deviation that is less than 5.0 minutes. A random sample of 15 students was selected and the sample standard deviation for the time needed to complete the exam was found to be 4.0 minutes. Using α=0.05, determine the critical value for this hypothesis test. Round to three decimal places.

Mathematics
2 answers:
Elodia [21]3 years ago
7 0

Answer:

The critical value for this hypothesis test is 6.571.

Step-by-step explanation:

In this case the professor wants to determine whether the average number of minutes that a student needs to complete a statistics exam has a standard deviation that is less than 5.0 minutes.

Then the variance will be, \sigma^{2}=(5.0)^{2}=25

The hypothesis to determine whether the population variance is less than 25.0 minutes or not, is:

<em>H</em>₀: The population variance is not less than 25.0 minutes, i.e. <em>σ²</em> = 25.

<em>Hₐ</em>: The population variance is less than 25.0 minutes, i.e. <em>σ²</em> < 25.

The test statistics is:

\chi ^{2}_{cal.}=\frac{ns^{2}}{\sigma^{2}}

The decision rule is:

If the calculated value of the test statistic is less than the critical value, \chi^{2}_{n-1} then the null hypothesis will be rejected.

Compute the critical value as follows:

\chi^{2}_{(1-\alpha), (n-1)}=\chi^{2}_{(1-0.05),(15-1)}=\chi^{2}_{0.95, 14}=6.571

*Use a chi-square table.

Thus, the critical value for this hypothesis test is 6.571.

Sholpan [36]3 years ago
7 0

Answer:

Critical value for this hypothesis test is 6.571

Step-by-step explanation:

We are given that a random sample of 15 students was selected and the sample standard deviation for the time needed to complete the exam was found to be 4.0 minutes.

A professor would like to test the hypothesis that the average number of minutes that a student needs to complete a statistics exam has a standard deviation that is less than 5.0 minutes.

So, Null Hypothesis, H_0 : \sigma = 5.0 minutes

Alternate Hypothesis, H_1 : \sigma < 5.0 minutes

Now, the test statistics used here for testing population standard deviation is;

           T.S. = \frac{(n-1) s^{2} }{\sigma^{2} } ~ \chi^{2} __n_-_1

where, s = sample standard deviation = 4.0 minutes

            n = sample size = 15

So, test statistics = \frac{(15-1) 4^{2} }{5^{2} } = 8.96

At, 5% level of significance the chi-square table gives critical value of 6.571 at 14 degree of freedom. Since our test statistics is more than the critical value as 8.96 > 6.571 so we have insufficient evidence to reject null hypothesis.

You might be interested in
How do I find the area of a composite figure
azamat
It depends on what the composite figure is, but use the formulas, such as A=1/2bh for the triangle and A=bh, for the square and the rectangle.
6 0
3 years ago
HELP ME PLZZ I NEED HELLPPP!!!!!1
marin [14]

Answer:

answer is not

Step-by-step explanation:

clear sorry

7 0
3 years ago
Read 2 more answers
Find the inverse of<br><br> f(x) = -6xˆ2 + 24x - 100
monitta

Answer:

See below

Step-by-step explanation:

y = -6x^2 + 24x-100

solve for 'x'

y + 100 =   -6x^2 + 24x   = -6(x^2-4x)    complete the square for x

(y+100) /(-6 ) =    (x-2)^2 -4                     add 4 to both sides

(y+100)/(-6) +4   = (x-2)^2                       sqrt both sides

sqrt [  ( y+100)/(-6) + 4  ]  + 2 = x           change  x and y

y = ± sqrt [ (x+100)/(-6) + 4 ] + 2            simplify (if needed)

<u>y  = ± sqrt( -x/6 -12.666)  + 2 </u>

5 0
2 years ago
Which statement best explains the relationship between numbers divisible by 5
adoni [48]
The answer is A) A number that is divisible by 10 is also divisible by 5 because all factors of 10 are also factors of 5.

hope this helps !
4 0
3 years ago
A 42 -ounce bottle of shampoo costs $2.52. Find the unit price
Ulleksa [173]
2.52/42 = 0.06 per oz
5 0
3 years ago
Other questions:
  • I NEED HELP NOW PLEASE!!!!!
    9·1 answer
  • I'm trying to pass my performance task and finish high school and I have no idea what it really is asking me to do, rather how t
    14·1 answer
  • One number added to three times another number is 24. Five times the first number added to three times to other number is 36. Fi
    5·1 answer
  • Consider the piecewise-defined function given by the graph. What are these values?
    9·2 answers
  • Help last question for math<br> What is:<br> -3/8 divided by 7/12?
    7·1 answer
  • Is 48 a solution to 2y = 24
    13·2 answers
  • Gezane is paid $3.25 for each toy she assembles. Last week she
    5·2 answers
  • PLEASE HELP ME WITH THIS
    10·1 answer
  • Please help me solve this !<br> will mark brainliest !<br> (spammers reported)
    8·2 answers
  • 4.
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!