Question

A candy manufacturer must monitor deviations in the amount of sugar in their products They want their products to meet standards. They selected a random sample of 20 candies and found that the sandard deviation of that sample is 1.7. What is the probabilty of finding a sample variance as high or higher if the population variance is actually 3277 Assume the population distribution is normal.

71

likes
354 views

Answer to a math question A candy manufacturer must monitor deviations in the amount of sugar in their products They want their products to meet standards. They selected a random sample of 20 candies and found that the sandard deviation of that sample is 1.7. What is the probabilty of finding a sample variance as high or higher if the population variance is actually 3277 Assume the population distribution is normal.

Expert avatar
Santino
4.5
111 Answers
To solve this problem, we can use the chi-squared distribution to test if the sample variance is significantly different from the population variance. The chi-squared distribution is commonly used to test the variances of two populations.

The test statistic for this problem is given by:

\chi^{2} = \frac{(n-1)S^{2}}{\sigma^{2}}

Where:
- \chi^{2} is the chi-squared value
- n is the sample size
- S^{2} is the sample variance
- \sigma^{2} is the population variance

In this case, we are interested in finding the probability of finding a sample variance as high or higher. This corresponds to the right-tail of the chi-squared distribution.

Step 1: Calculate the chi-squared value
Using the given values, we have:
n = 20
S^{2} = (1.7)^{2} = 2.89
\sigma^{2} = 3277

Plugging these values into the formula, we get:
\chi^2=\frac{(20-1)(2.89)}{3277}\approx0.0168

Step 2: Find the probability
To find the probability of finding a sample variance as high or higher, we need to find the right-tail probability of the chi-squared distribution.

The degrees of freedom for the chi-squared distribution in this case is n-1 = 19 .

Using a chi-squared table or a calculator, we can find that the right-tail probability for \chi^{2} = 0.0168 with df = 19 is approximately 0.9384.

Answer:
The probability of finding a sample variance as high or higher if the population variance is actually 3277 is approximately 1.

Frequently asked questions (FAQs)
What is the value of sin(45°) + cos(30°) / tan(60°)
+
What is the median of the set of numbers: 3, 5, 7, 9, 11?
+
What is the equation of a hyperbola with vertices at (-4,0) and (4,0), and foci at (-6,0) and (6,0)?
+
New questions in Mathematics
Y=-x^2-8x-15 X=-7
What is the amount of interest of 75,000 at 3.45% per year, at the end of 12 years and 6 months?
(6.2x10^3)(3x10^-6)
The main cost of a 5 pound bag of shrimp is $47 with a variance of 36 if a sample of 43 bags of shrimp is randomly selected, what is the probability that the sample mean with differ from the true mean by less than $1.4
∫ √9x + 1 dx
A mutual fund manager has a $350 million portfolio with a beta of 1.10. The risk-free rate is 3.5%, and the market risk premium is 6.00%. The manager expects to receive an additional $150 million which she plans to invest in several different stocks. After investing the additional funds, she wants to reduce the portfolio’s risk level so that once the additional funds are invested the portfolio’s required return will be 9.20%. What must the average beta of the new stocks added to the portfolio be (not the new portfolio’s beta) to achieve the desired required rate of return?
Use a pattern to prove that (-2)-(-3)=1
A machine produces 255 bolts in 24 minutes. At the same rate, how many bolts would be produced in 40 minutes?
Take the limit of (sin(x-4))/(tan(x^2 - 16) as x approaches 4.
Find the zero of the linear function 8x + 24 = 0
Find the vertex F(x)=x^2-10x
What is the total amount due and the amount of interest on a 3-year loan of $1,000 at a simple interest rate of 12% per year?
How do you convert a fraction to a decimal
22. Let [AB] be a chord in a circle C, and k a circle which is internally tangent to the circle C at a point P and to the chord [AB] at a point Q. Show that the line P Q passes through the midpoint of the arc AB opposite to the arc APB.
A 20-year old hopes to retire by age 65. To help with future expenses, they invest $6 500 today at an interest rate of 6.4% compounded annually. At age 65, what is the difference between the exact accumulated value and the approximate accumulated value (using the Rule of 72)?
56 × 12 = 672. How should you adjust this answer 672 to determine 57 × 12? a) The answer increases by 1 b) The answer increases by 57 c) The answer increases by 56 d) The answer increases by 12
The slope of the tangent line to the curve f(x)=4tan x at the point (π/4,4)
Define excel and why we use it?
Triangle ABC has AB=AC and angle BAC =X, with X being less than 60 degrees. Point D lies on AB such that CB = CD Point E lies on AC such that CE= DE Determine angle DEC in terms of X
x(squared) -8x=0