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
kkurt [141]
3 years ago
7

The sugar content of the syrup in canned peaches is normally distributed. A random sample of n = 10 cans yields a sample standar

d deviation of s = 4.798 milligrams. Construct a 95% two-sided confidence interval for σ. Round your answers to 2 decimal places.
Mathematics
1 answer:
Serggg [28]3 years ago
7 0

Answer:

The 95% confidence interval is given by:

3.30<σ<8.76

Step-by-step explanation:

1) Data given and notation

s=4.798 represent the sample standard deviation

\bar x represent the sample mean

n=10 the sample size

Confidence=95% or 0.95

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

df=n-1=10-1=9

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a tabel to find the critical values.  

The excel commands would be: "=CHISQ.INV(0.025,9)" "=CHISQ.INV(0.975,9)". so for this case the critical values are:

\chi^2_{\alpha/2}=19.022

\chi^2_{1- \alpha/2}=2.700

And replacing into the formula for the interval we got:

\frac{(9)(4.798)^2}{19.022} \leq \sigma \frac{(9)(4.798)^2}{2.700}

10.892 \leq \sigma^2 \leq 76.736

Now we just take square root on both sides of the interval and we got:

3.30 \leq \sigma \leq 8.76

So the best option would be:

3.30<σ<8.76

You might be interested in
Frank's paper airplane glided 78.9 m. Sarah's plane glided 85 m. How many more centimeters did Sarah's plane glide? 1 m= 100 cm
Olegator [25]

Answer:

610 cm

Step-by-step explanation:

78.9 x 100 = 7890 cm  85 x 100 = 8,500 cm        

8,500 - 7890 = 610 cm

4 0
2 years ago
Eddie needs 2 2/3 cups of flour for one batch of pancakes. How much flour does he need for 2 1/2 batches?
Alexxandr [17]

for 1 batch of pancake = 2 2/3 = 8/3 cups

for 2 1/2 = 5/2 pancake = 8/3 * 5/2 = 40/6 cups = 6 4/6 cups

7 0
3 years ago
Read 2 more answers
What is this plz help
Aliun [14]

Answer:

x ≤ 3

Step-by-step explanation:

Given

2(4 + 2x) ≥ 5x + 5 ← distribute parenthesis on left side

8 + 4x ≥ 5x + 5 ( subtract 4x from both sides )

8 ≥ x + 5 ( subtract 5 from both sides )

3 ≥ x , then

x ≤ 3

7 0
3 years ago
The California Tiger Salamander is an endangered species, which decreases at the rate of 4.6% per year in a habitat that current
stellarik [79]

Answer:

Population after 4 years = 49 (nearest unit)

Population after 5 years  = 47 (nearest unit)

Step-by-step explanation:

Yearly decrease = 4.6%

Decrease factor (what's left) = (100-4.6)% = 0.954

Current population, P = 60

population after n years = P(0.954)^n  (to the nearest unit)

Population after 4 years = 60(0.954)^4 = 49.7 = 49 (nearest unit)

Population after 5 years  = 60(0.954)^5 = 47.4 = 47 (nearest unit)

5 0
3 years ago
Read 2 more answers
1 /3 + 1 /9 / (7/10 * 5 / 4 )
Ludmilka [50]

Answer:

0.46

Hope it helps..

have a great day : )

7 0
3 years ago
Other questions:
  • Seven more than the cube of a number is what
    13·1 answer
  • Pls help............Thanks
    10·1 answer
  • What is fraction 5/33 in a decimal form
    11·2 answers
  • Which best describes this triangle? A. All sides are different lengths; one angle is obtuse. B. All sides are equal; all angles
    15·2 answers
  • Tell whether the ordered pair is a solution of the linear system
    7·1 answer
  • N - 4 = 3n + 6 Yikesss
    5·2 answers
  • A laser tag park charges $15 per person.If Sammy can spend up to $120,how many friends can he invite
    6·2 answers
  • 56 is what percent of 72 <br><br> Integer fraction or mixed number
    5·2 answers
  • PLEASE SOLVE QUICK. I NEED THIS FOR MY QUIZ NOW
    14·2 answers
  • ANYONE PLS HELP ASAP!!!
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!