estimate the mean amount spent ($) on a certain retail website by members of the website's premium program. A random sample of 97 members of the website's premium program who recently made a purchase on the website yielded a mean of $1900 and a standard deviation of $300. Complete parts (a) and (b) below. Question content area bottom Part 1 a. Construct a 99% confidence interval estimate for the mean spending for all shoppers who are members of the website's premium program. enter your response here≤μ≤enter (Round to two decimal places as needed.) Part 2 b. Interpret the interval constructed in (a). Choose the correct answer below. A.With 99% confidence, the mean spending in dollars for all shoppers who are members of the website's premium program is between the lower and upper limits of the confidence interval. B.99% of all shoppers who are members of the website's premium program have spent an amount in dollars that is between the lower and upper limits of the confidence interval. C.There is a 99% probability that mean spending in dollars for all shoppers who are members of the website's premium program is between the lower and upper limits of the confidence interval. D.The sample mean spending in 99%of all samples of 97members of the website's premium program will be between the lower and upper limits of the confidence interval.

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 content area bottom

Part 1

a. Construct a

99%

confidence interval estimate for the mean spending for all shoppers who are members of the website's premium program.

enter your response here≤μ≤enter (Round to two decimal places as needed.)

Part 2

b. Interpret the interval constructed in (a).

Choose the correct answer below.

A.With 99% confidence, the mean spending in dollars for all shoppers who are members of the website's premium program is between the lower and upper limits of the confidence interval.

B.99% of all shoppers who are members of the website's premium program have spent an amount in dollars that is between the lower and upper limits of the confidence interval.

C.There is a 99% probability that mean spending in dollars for all shoppers who are members of the website's premium program is between the lower and upper limits of the confidence interval.

D.The sample mean spending in 99%of all samples of 97members of the website's premium program will be between the lower and upper limits of the confidence interval.

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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