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
Archy [21]
3 years ago
11

A random sample of 25 boxes of cereal have a mean of 372.5grams and a standard deviation of 15 grams. Does an average box of cer

eal contain more than 368 grams of cereal? Test hypothesis at the 5% significance level, outline all steps involved. (9mks)​
Mathematics
1 answer:
ss7ja [257]3 years ago
6 0

Using the t-distribution, it is found that since the <u>test statistic is less than the critical value for the right-tailed test</u>, there is not enough evidence to conclude that an average box of cereal contain more than 368 grams of cereal.

At the null hypothesis, it is <u>tested if the average box of cereal does not contain more than 368 grams</u>, that is:

H_0: \mu \leq 368

At the alternative hypothesis, it is <u>tested if it contains</u>, that is:

H_1: \mu > 368

We have the <em>standard deviation for the sample</em>, hence, the t-distribution is used to solve this question.

The test statistic is given by:

t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}

The parameters are:

  • \overline{x} is the sample mean.
  • \mu is the value tested at the null hypothesis.
  • s is the standard deviation of the sample.
  • n is the sample size.

In this problem, the values of the <em>parameters </em>are: \overline{x} = 372.5, \mu = 368, s = 15, n = 25.

Hence, the value of the <em>test statistic</em> is:

t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}

t = \frac{372.5 - 368}{\frac{15}{\sqrt{25}}}

t = 1.5

The critical value for a <u>right-tailed test</u>, as we are testing if the mean is greater than a value, with a <u>significance level of 0.05,</u> with 25 -1 = <u>24 df</u>, is of t^{\ast} = 1.71.

Since the <u>test statistic is less than the critical value for the right-tailed test</u>, there is not enough evidence to conclude that an average box of cereal contain more than 368 grams of cereal.

You can learn more about the use of the t-distribution to test an hypothesis at brainly.com/question/13873630

You might be interested in
The length of a rectangular garden is 7 meters longer than its width. if its perimeter is ( 12 x + 14) meters, find its length i
cluponka [151]
L=7+w
P=(12x+14)=2(6x+7)
l+w= P/2 = 2(6x+7)/2= 6x+7
l+w=6x+7
2l = 6x+7
l = (6x+7)/2
l=7+w
-> w= l-7
= [(6x+7)/2] -7
= (6x+7-14)/2
= (6x-7)/2

7 0
3 years ago
What is the answer to 3 and 5 7ths - 3 and 2 sevanths
Sergeeva-Olga [200]
Its 3/7
\frac{3}{7}
4 0
3 years ago
Read 2 more answers
Ayo i need help on math <br> 3x-45=12
Leto [7]

x=19

add 45 to both sides 3

6 0
3 years ago
Helppp plsssss!!show your work.<br>Thanks
gregori [183]

You are basically just adding, so combine like terms.

3x^2 + 5x^2 = 8x^2

6x - 2x = 4x

4 - 8 = -4

So the answer is D.

8 0
3 years ago
Read 2 more answers
Please help!!! Find the equation for all 4!!! It needs to be <br> Y=mx +b
emmainna [20.7K]
1) y= 2/5x -3
2) y= 2/3x + 1
3) y= 2x -1
4) y= 5/4x + 3
I think
7 0
3 years ago
Other questions:
  • Tom received a coupon in the mail for 30%off one regular priced item for a local sporting goods store He wishes tp purchase a so
    5·1 answer
  • What is the area of the triangle
    11·1 answer
  • Find a report in a newspaper magazine or on the Internet that uses results from a servery. Evaluate how the survey uses ratios t
    5·1 answer
  • 1 How many 1/3s or "thirds” are there between 0 and 1 on a number line?<br> How do you know?
    14·1 answer
  • A rectangular box with a volume of 684 ftcubed is to be constructed with a square base and top. The cost per square foot for the
    12·1 answer
  • 3 x 16 divided by 2-1
    7·1 answer
  • I don’t understand can you help
    15·1 answer
  • Help as soon as possible!!<br><br> Answer only if you know! <br><br> At least answer one of them!
    6·1 answer
  • Hey ! Can anyone help me with this problem please thank you !!
    11·1 answer
  • PLS HELP DUE TODAY 11:59
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!