A zookeeper took a random sample of 30 days and observed how much food an elephant ate on each of those days. The sample mean was 350kg and standard deviation was 25kg. The resulting 90% CI for the mean amount of food was [341kg, 359kg]. Which of the following statements is a correct interpretation of the 90% CI?A.There is a 0.9 probability that the true mean amount of food is between 341kg and 359kg.B.In repeated sampling, the method produces confidence intervals that capture the population mean in about 90% of the samples. C.In repeated sampling, this method produces a sample mean of 341kg and 359kg. D.The elephant ate between 341kg and 359kg on 90% of all the days.

Given : 90% CI for the mean amount of food was [341kg, 359kg].

Answered: zookeeper took a random sample of 30…

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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A zookeeper took a random sample of 30 days and observed how much food an elephant ate on each of those days. The sample mean was 350kg and standard deviation was 25kg. The resulting 90% CI for the mean amount of food was [341kg, 359kg]. Which of the following statements is a correct interpretation of the 90% CI?

There is a 0.9 probability that the true mean amount of food is between 341kg and 359kg.

In repeated sampling, the method produces confidence intervals that capture the population mean in about 90% of the samples.

In repeated sampling, this method produces a sample mean of 341kg and 359kg.

The elephant ate between 341kg and 359kg on 90% of all the days.

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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