A sample of 31 boxes of cereal has a sample standard deviation of 0.81 ounces. Construct a 93% confidence interval to estimate the true standard deviation of the fllins process for the boxes of cereal. a (0433, 1.120) b)(0.658,1.058) c (0.525, 1095) d (0.731,0.731) e) None of the above.
Answers
Final answer:
Using the chi-square distribution and given data, a 93% confidence interval for the standard deviation is found to be (0.525, 1.095). Therefore, the correct answer is option (c).
Explanation:
To construct a confidence interval to estimate the true standard deviation of the filling process for the boxes of cereal, we will use the chi-square distribution as it is used when dealing with standard deviation and variance.
The formula for the confidence interval in this case is: (sqrt((n-1)*s^2/chi2(upper)), sqrt((n-1)*s^2/chi2(lower))), where n is the sample size, s is the sample standard deviation and chi2 is the chi-square value for the corresponding degrees of freedom and confidence level.
In this case, we have n=31, s=0.81. The degrees of freedom are one less than the sample size, so df = 31 - 1 = 30. For a 93% confidence level, the chi-square values are X2(0.035, 30) = 21.92 and X2(0.965, 30) = 41.34.
Substituting these values into the formula, we get: (sqrt((31-1)*(0.81)^2/41.34), sqrt((31-1)*(0.81)^2/21.92)) = (0.525, 1.095). Hence, the correct answer is (c) (0.525, 1.095).
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Final answer:
The 93% confidence interval for the standard deviation of the filling process for the boxes of cereal is (0.658,1.058), which is choice (b). The solution is determined using chi-square distribution and the formula for constructing a confidence interval specifically for standard deviations.
Explanation:
To answer this question, we will use chi-square distribution which is commonly used to construct a confidence interval for standard deviations.
The formula for a confidence interval in this case is ( √((n-1)s² / χ²_(1 - α/2)), √((n-1)s² / χ²_(α/2)) ). Here, n is the sample size, s is the sample standard deviation, α is the significance level (1 - confidence level). χ² represents chi-square values, where α/2 and 1 - α/2 are the confidence levels for a two-tailed test.
Using the chi-square table, for n - 1 = 30 degrees of freedom, we find the chi-square value for (1 - α/2)=0.935 is 17.708 and the chi-square value for α/2=0.065 is 46.194. Substituting n = 31, s = 0.81 into the formula, we get the 93% confidence interval for the standard deviation of the filling process for the boxes of cereal as ( √((30*0.81²) / 46.194), √((30*0.81²) / 17.708) ) = (0.658, 1.058).
So, the correct answer is (b) (0.658,1.058).
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Related Questions
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Answers
Answer:
Wideness ≈ 40 m
He will be able to do it .
Step-by-step explanation:
He wants to estimate the width of a river so he can get to the other side to save the world . The width of the river is the side AB. From the scale above 2 right angle triangle are formed . The smaller triangle is CDE and the larger triangle is CAB.
The angle ECD can be gotten below
tan C = opposite/adjacent
tan C = 8/6
tan C = 1.3333
C = tan⁻¹ 1.333
C = 53.1301022854
C = 53. 13°
∠ACB = ∠ECD (vertically opposite angles)
Using the angle to find the wideness of the river AB in triangle CAB.
tan C = opposite/adjacent
tan 53.13° = AB/30
AB = 30 tan 53.13
AB = 30 × 1.33332837108
AB = 39.9998511323
AB ≈ 40 m
He will be able to do it.
Answers
Answer:
Correct option: "No, a probability of about 0.20 would be assigned using the relative frequency method if selection is equally likely."
Step-by-step explanation:
The assumption made is that all the 5 different packages are equally likely, i.e. the probability of selecting a package is .
The probability distribution is shown below.
According to the probability distribution:
- The probability of a person preferring design 1 is,
- The probability of a person preferring design 2 is,
- The probability of a person preferring design 3 is,
- The probability of a person preferring design 4 is,
- The probability of a person preferring design 1 is,
So it can be seen that the probability of preferring any of the 5 designs are not same.
Thus, the designs are not equally likely.
The correct option is "No, a probability of about 0.20 would be assigned using the relative frequency method if selection is equally likely."
The selection Probability determined using the relative frequency method do not match the assigned probabilities, suggesting that the data do not confirm the belief that one design is as likely to be selected as another.
The given data can be used to calculate the relative frequencies of each package design selected by the consumers.
To determine the selection probabilities using the relative frequency method, divide the number of times a design was preferred by the total number of consumers.
For example, for design 1, the selection probability would be 10/100 = 0.1.
Similarly, for design 2, the selection probability would be 5/100 = 0.05.
The selection probabilities for designs 3, 4, and 5 would be 0.3, 0.4, and 0.15 respectively.
Comparing these probabilities to the assigned probabilities, it can be observed that the assigned probabilities do not match the observed relative frequencies, indicating that the data do not confirm the belief that one design is just as likely to be selected as another.
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Answers
Answer:
I believe the answer is 406 miles.
Let me know of this is the correct answer
many students are registered in Bob's class?
Answers
12/4=?/1
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Answer: 3/1
Step-by-step explanation:
Your supposed to divide by 4 on the top and bottom.
12 4= 3
4 4 = 1
Answers
.. n + 7
for n = 100
.. 100 +7
.. = 107
The 100th term is 107.