A report states that the mean yearly salary offer for students graduating with mathematics and statistics degrees is $62,925. Suppose that a random sample of 50 mathematics and statistics graduates at a large university who received job offers resulted in a mean offer of $63,200 and a standard deviation of $3,500. Do the sample data provide strong support for the claim that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,925? Test the relevant hypotheses using ? = 0.05. a. Find the test statistic and P-value. (Use technology to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value = b.State your conclusion. a. Fail to reject H0. We have convincing evidence that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,925. b. Reject H0. We have convincing evidence that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,925. c. Fail to reject H0. We do not have convincing evidence that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,925. d. Reject H0. We do not have convincing evidence that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,925.

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Description: A report states that the mean yearly salary offer for students graduating with mathematics and statistics degrees is $62,925. Suppose that a random sample of 50 mathematics and statistics graduates at a large university who received job offers result

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Answered: the relevant hypotheses using ? =…

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 report states that the mean yearly salary offer for students graduating with mathematics and statistics degrees is $62,925. Suppose that a random sample of 50 mathematics and statistics graduates at a large university who received job offers resulted in a mean offer of $63,200 and a standard deviation of $3,500. Do the sample data provide strong support for the claim that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,925? Test the relevant hypotheses using

? = 0.05.

Find the test statistic and P-value. (Use technology to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)

t	=
P-value	=

State your conclusion.

a. Fail to reject H₀. We have convincing evidence that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,925.

b. Reject H₀. We have convincing evidence that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,925.

c. Fail to reject H₀. We do not have convincing evidence that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,925.

d. Reject H₀. We do not have convincing evidence that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,925.

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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