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
Musya8 [376]
3 years ago
11

The amounts of vitamin C (in milligrams) for 100g (3.57 ounces) of various randomly selected fruits and vegetables are listed. I

s there sufficient evidence to conclude that the standard deviation differs from 12 mg? Use alpha = 0.10. Use a graphing calculator
Mathematics
1 answer:
Gelneren [198K]3 years ago
7 0

Answer:

The values are missing in the question. They are : 16.3,12.8,13,32.2,28.1,34.4,46.4,53,15.4,18.2

Step-by-step explanation:

16.3,12.8,13,32.2,28.1,34.4,46.4,53,15.4,18.2

We calculate sample mean and std deviation from given data.

Sample Mean, $ {\overset{-}X} =\frac{\Sigma (X)}{n} $   =269.8/10=26.98

Sample Variance, $s^2= \frac{\Sigma(X-{\overset{-}X})^2}{(n-1)}$    =1859.496/9=206.610667

Sample std dev,s=$\sqrt{s^2}$=√206.610667≈14.373958

We want to test two tailed hypothesis:

$H_0$ : σ=12

$H_2$ : σ≠12

Given: s=14.373958⇒ $s^2$ =206.610667,n=10

Significance level, a=0.1 Degrees of freedom, df=n-1=9

Since this is two tailed test, we need area of α=0.1 on either side of critical value. This means area of 0.05 on right of positive critical value.

Critical values are given by $ X_{1-\alpha/2}^2 =X_{0.95}^2 \text{ and}\ X_{1-\alpha/2}^2 =X_{0.95}^2 $  with 9 degrees of freedom.

We can use chi-square table or following excel commands:

CHISQ. INV(0.95,9)=3.32511284307

CHISQ. INV (0.05,9)=16.9189776046

Critical Values, $X_L^2$=3.325  and $X_R^2$=16.919

Since this is two tailed test, the decision rule or rejection criteria is:

Reject null hypothesis if test statistic is less than or equal to left critical value OR more than or equal to right critical value, i.e,

Reject $H_0$   if $x^2$≤3.325  OR $x^2$≥16.919

Test statistic is given by $X^2=\frac{(n-1)s^2}{\sigma^2}$ =((9)*206.610667)/144=12.913167    

Test statistic, $x^2$=12.913

since test statistic is between two critical values, we (do not reject $H_0$) (i.e, we fail to reject $H_0$.

Conclusion: There is (not sufficient) evidence to conclude that standard deviation is not equal to 12 .

Alternatively, we can use p-value approach. The decision rule or rejection criteria is: reject null hypothesis if p-value is less than or equal to significance level (α), i.e, reject $H_0$ if p-value ≤0.1

P-value is twice the (smaller) tail area of test statistic because this is two tailed test. We can use excel function to find this. 2*M IN (CHISQ.DIST (12.913167,9,  TRUE ) 1-CHISQ.DIST 12.913167,9,  TRUE ) =0.333149809868

P-value =0.3331

since p-value is greater than significance level (α),we (do not reject $H_0$) (i.e, we fail to reject $H_0$).

Conclusion: There is (not sufficient) evidence to conclude that standard deviation is different from 12 .

 

You might be interested in
30<br> Solve by elimination:<br> 2x - 3y = -6<br> -2x - 2y = 26 ,
Arturiano [62]

Answer:

x=-9,y=-4

Step-by-step explanation:

2x-3y=-6...(1)

-2x-2y=26...(2)

To solve we will have to eliminate one of the given variables, the variable to be eliminated is x

And it can be done by adding up (1) and (2)

It gives

-5y=20

Divide both sides by-5

y=-4

Then substitute the value of y into (1)

2x-3(-4)=-6

2x+12=-6

Substrate 12 from both sides

2x=-18

Divide both sides by 2

x=-9

Therefore x gives -9 and y gives-4

5 0
3 years ago
Use the digits in the number 531,642 to write a number that is greater than and a number that is less than 531,642.
Nookie1986 [14]
642,531 is greater than 135,246
8 0
3 years ago
What is the distance between (5,8) and (2,4) by using distance formula
Dimas [21]

Answer:

Distance = 5

Step-by-step explanation:

D= sqrt (x1-x2)^2 + (y1-y2)^2

(5-2)^2 + (8-4)^2=3^2 + 4 ^2 = 9 +16 = 25

Sqrt of 25 = 5

Distance = 5

Hope this helps

7 0
3 years ago
Read 2 more answers
Find the mode of the data.<br> 1, 2, 1, 3, 3, 4, 1<br> The mode is
drek231 [11]

Answer:

1 is the answer.

Step-by-step explanation:

The mode of a data set is the number that occurs most frequently in the set.

5 0
2 years ago
Read 2 more answers
The cost of a service or item is a(n):<br><br> 1. Expense<br> 2. Income<br> 3. Coupon<br> 4. Budget
miv72 [106K]
<span>The cost of a service or item is an expense
</span>
5 0
2 years ago
Other questions:
  • How do you draw a model that shows decimal 1.7
    7·2 answers
  • 3. A balloon with a small leak loses 0.5% of its volume each day. If it originally contained 40 liters of gas, what is the volum
    8·1 answer
  • Is it 1,2,3 or 4? help please
    9·1 answer
  • If earl runs 25 meters in 10 seconds how many meters does earl run per second?
    12·2 answers
  • Given the function, d(t) = 50t, the variable t represents which of the following? Select all that apply. input output function i
    5·2 answers
  • Mindy's mother filled her car's gas tank with 10.4 gallons of gasoline. If the gasoline cost $3.35 per gallon, how much did Mind
    12·2 answers
  • What is 7×111 plsssss help me I feel like it's sooo easy I'm making it hard
    6·2 answers
  • Which two ratios form a proportion?
    11·2 answers
  • If 15 of the 1001<br> cars in a parking<br> lot are white,<br> how many cars<br> are white?
    13·2 answers
  • Pls explain why its a yes pleasee and thx u​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!