Answered: Determine the 95% 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

Two researchers conducted a study in which two groups of students were asked to answer 42 trivia questions from a board game. The students in group 1 were asked to spend 5 minutes thinking about what it would mean to be a professor, while the students in group 2 were asked to think about soccer hooligans. These pretest thoughts are a form of priming. The 200 students in group 1 had a mean score of 23.5 with a standard deviation of 4.3, while the 200 students in group 2 had a mean score of 17.7 with a standard deviation of 4.1.

Complete parts (a) and (b) below.

(a) Determine the 95% confidence interval for the difference in scores, μ1−μ2. Interpret the interval.

The lower bound is __.

The upper bound is ___

(Round to three decimal places as needed.)

B Interpret the interval. Choose the correct answer below.

A. The researchers are 95% confident that the difference of the means is in the interval.

B. There is a 95% probability that the difference of the means is in the interval.

C. The researchers are 95% confident that the difference between randomly selected individuals will be in the interval.

D. There is a95% probability that the difference between randomly selected individuals will be in the interval.

(b) What does this say about priming?

A. Since the 95% confidence interval does not contain zero, the results suggest that priming does have an effect on scores.

B. Since the 95% confidence interval contains zero, the results suggest that priming does not have an effect on scores.

C. Since the 95% confidence interval does not contain zero, the results suggest that priming does not have an effect on scores.

D. Since the 95% confidence interval contains zero, the results suggest that priming does have an effect on scores.

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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