Answered: A statistics instructor randomly…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

A statistics instructor randomly selected four bags of oranges, each bag labeled 10 pounds, and weighed the bags. They weighed 10.6,10.9,10.7, and 10.8 pounds. Assume that the distribution of weights is Normal. Find a 95% confidence interval for the mean weight of all bags of oranges. Use technology for your calculations. Answer parts a and b below.

a. Choose the correct interpretation of the confidence interval below and, if necessary, fill in the answer boxes to complete your choice. (Type integers or decimals rounded to the nearest thousandth as needed. Use ascending order.)

b. Does the interval capture 10 pounds? Is there enough evidence to reject the null hypothesis that the population mean weight is 10 pounds? Explain your answer.

A statistics instructor randomly selected four bags of oranges, each bag labeled 10 pounds, and weighed the bags. They weighed 10.6, 10.9, 10.7, and 10.8 pounds. O Assume that the distribution of weights
is Normal. Find a 95% confidence interval for the mean weight of all bags of oranges. Use technology for your calculations. Answer parts a and b below.
A. There is a 95% chance that all intervals will be between
and
B. We are 95% confident that the sample mean is between
and
C. We are 95% confident the population mean is between
and
O D. The requirements for constructing a confidence interval are not satisfied.
(Type integers or decimals rounded to the nearest thousandth as needed. Use ascending order.)
b. Does the interval capture 10 pounds? Is there enough evidence to reject the null hypothesis that the population mean weight is 10 pounds? Explain your answer.
A. Yes, it does capture 10. Do not reject the claim of 10 pounds because 10 is in the interval.
B. No, it does not capture 10. Do not reject the claim of 10 pounds because 10 is not in the interval.
C. Yes, it does capture 10. Reject the claim of 10 pounds because 10 is in the interval.
O D. No. it does not capture 10. Reiect the claim of 10 pounds because 10 is not in the interval.
O O C

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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