Confidence Interval A simple random sample of 41 Veterans Day celebrations was selected and the number of children attending each was recorded. The mean number of children in attendance for this sample of 41 Veterans Day celebrations was 72, with a standard deviation of 9.4. If appropriate, use this information to calculate and interpret a 98% confidence interval for the mean number of children attending all 2017 Veterans Day celebrations. Using 98% confidence, which of the following is the correct confidence statement? a) We have 98% confidence that the mean number of children attending all 2017 Veterans Day celebrations is between is between 56.27 and 61.73 b) We have 98% confidence that the mean number of children attending all 2017 Veterans Day celebrations is between 68.443 and 75.557. c) We have 98% confidence that the mean number of children attending all 2017 Veterans Day celebrations is between is between 48.992 and 59.008. d) We have 98% confidence that the mean number of children attending all 2017 Veterans Day celebrations is between is between 68.5 and 75.415 e) We have 98% confidence the mean number of children attending all 2017 Veterans Day celebrations is between is between 49.31 and 58.69. Is the mean number of children attending all 2017 Veterans Day celebrations in the confidence interval computed in question above? a) I don't know b) No c) True d) Yes In the question above a 98% confidence interval was computed based on a sample of 41 Veterans Day celebrations. If the confidence level were decreased to 90%, what impact would this have on the margin of error and width of the confidence interval? a) The margin of error would increase and the width would decrease. b) Neither the margin of error nor the width would be affected. c) Both the margin of error and the width would increase.

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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Confidence Interval

A simple random sample of 41 Veterans Day celebrations was selected and the number of children attending each was recorded. The mean number of children in attendance for this sample of 41 Veterans Day celebrations was 72, with a standard deviation of 9.4. If appropriate, use this information to calculate and interpret a 98% confidence interval for the mean number of children attending all 2017 Veterans Day celebrations.

Using 98% confidence, which of the following is the correct confidence statement?

a) We have 98% confidence that the mean number of children attending all 2017 Veterans Day celebrations is between is between 56.27 and 61.73

b) We have 98% confidence that the mean number of children attending all 2017 Veterans Day celebrations is between 68.443 and 75.557.

c) We have 98% confidence that the mean number of children attending all 2017 Veterans Day celebrations is between is between 48.992 and 59.008.

d) We have 98% confidence that the mean number of children attending all 2017 Veterans Day celebrations is between is between 68.5 and 75.415

e) We have 98% confidence the mean number of children attending all 2017 Veterans Day celebrations is between is between 49.31 and 58.69.

Is the mean number of children attending all 2017 Veterans Day celebrations in the confidence interval computed in question above?

a) I don't know

b) No

c) True

d) Yes

In the question above a 98% confidence interval was computed based on a sample of 41 Veterans Day celebrations. If the confidence level were decreased to 90%, what impact would this have on the margin of error and width of the confidence interval?

a) The margin of error would increase and the width would decrease.

b) Neither the margin of error nor the width would be affected.

c) Both the margin of error and the width would increase.

d) Both the margin of error and the width would decrease.

e) The margin of error would decrease and the width would increase.

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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