Answered: The confidence interval is ,. (Round…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 11PT

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Question

The data below shows the sugar content in grams of several brands of children's and adults' cereals. Create and interpret a 95% confidence interval for the difference in the mean sugar content,

μC−μA.

Be sure to check the necessary assumptions and conditions. (Note: Do not assume that the variances of the two data sets are equal.)

Full data set

Children's cereal:

42.1,

57.7,

49.8,

44.6,

52.4,

47.6,

51.3,

44.6,

42.7,

44.7,

48.4,

43.8,

37.8,

59,

46.4,

53.2,

35.6,

56.7,

43.9,

32.9

Adults' cereal:

24.7,

27.8,

1.5,

7.2,

3.5,

24.9,

16.8,

14.7,

22.9,

8.1,

6.2,

12.4,

18.6,

14.4,

2.8,

15.4,

0.3,

0.9,

1.9,

8.3,

13.7,

0.3,

0.9,

16.9,

8.1,

16.2,

12.4

The confidence interval is ,.

(Round to two decimal places as needed.)

Interpret the confidence interval. Select the correct choice below and fill in the answer boxes to complete your choice.

(Round to two decimal places as needed.)

Based on these samples, with 95% confidence, adult's cereals average between the lower boundary of

nothing

and upper boundary of

nothing

more grams of sugar content than children's cereals.

Based on these samples, with 95% confidence, children's cereals average between the lower boundary of

nothing

and upper boundary of

nothing

more grams of sugar content than adult's cereals.

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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