A sample of 13 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weight of each bag was then recorded. The mean weight was 3 ounces with a standard deviation of 0.13 ounces. The population standard deviation is known to be 0.1 ounce. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)SUBPARTPlease label each part. O Part (e)Construct a 90% confidence interval for the population mean weight of the candies.(i) State the confidence interval. (Round your answers to three decimal places.)(ii) Sketch the graph.aC.L. =22(iii) Calculate the error bound. (Round your answer to three decimal places.)Part (f)Part (g)In complete sentences, explain why the confidence interval in part (f) is larger than the confidence interval in part (e).The confidence interval in part (f) is larger than the confidence interval in part (e) because the mean weight changes for each sample.The confidence interval in part (f) is larger than the confidence interval in part (e) because the population standard deviation changes for each sample.The confidence interval in part (f) is larger than the confidence interval in part (e) because a small sample size is being used.The confidence interval in part (f) is larger than the confidence interval in part (e) because a larger level of confidence increases the error bound, making the interval larger.O Part (h)In complete sentences, give an interpretation of what the interval in part (f) means.We are 98% confident that the mean weight of the sample of 13 small bags of candies is between these values.We are 98% confident that a small bag of candies weighs between these values.There is a 98% chance that a small bag of candies weighs between these values.We are 98% confident that the true population mean weight of all small bags of candies is between these values.O O O OO O

Answered: A sample of 13 small bags of the same…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 58E: What is meant by the sample space of an experiment?

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A sample of 13 small bags of the same brand of candies was selected. Assume that the population distribution of bag weights is normal. The weight of each bag was then recorded. The mean weight was 3 ounces with a standard deviation of 0.13 ounces. The population standard deviation is known to be 0.1 ounce.

NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

SUBPART

Please label each part.

O Part (e)
Construct a 90% confidence interval for the population mean weight of the candies.
(i) State the confidence interval. (Round your answers to three decimal places.)
(ii) Sketch the graph.
a
C.L. =
2
2
(iii) Calculate the error bound. (Round your answer to three decimal places.)
Part (f)
Part (g)
In complete sentences, explain why the confidence interval in part (f) is larger than the confidence interval in part (e).
The confidence interval in part (f) is larger than the confidence interval in part (e) because the mean weight changes for each sample.
The confidence interval in part (f) is larger than the confidence interval in part (e) because the population standard deviation changes for each sample.
The confidence interval in part (f) is larger than the confidence interval in part (e) because a small sample size is being used.
The confidence interval in part (f) is larger than the confidence interval in part (e) because a larger level of confidence increases the error bound, making the interval larger.
O Part (h)
In complete sentences, give an interpretation of what the interval in part (f) means.
We are 98% confident that the mean weight of the sample of 13 small bags of candies is between these values.
We are 98% confident that a small bag of candies weighs between these values.
There is a 98% chance that a small bag of candies weighs between these values.
We are 98% confident that the true population mean weight of all small bags of candies is between these values.
O O O O
O O

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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