A college professor claims that the entering class this year appears to be smarter than entering classes from previous years. He tests a random sample of 16 of this year's entering students and finds that their mean IQ score is 116, with a standard deviation of 15. The college records indicate that the mean IQ score for entering students from previous years is 112. If we assume that the IQ scores of this year's entering class are normally distributed, is there enough evidence to conclude, at the 0.05 level of significance, that the mean IQ score, μ, of this year's class is greater than that of previous years? Perform a one-tailed test and answer questions. Carry your intermediate computations to at least three decimal places and round your answers. The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: (Choose one) Z t Chi square F The value of the test statistic: (Round to at least three decimal places.) The critical value at the 0.05 level of significance: (Round to at least three decimal places.) Can we conclude, using the 0.05 level of significance, that the mean IQ score of this year's class is greater than that of previous years? Yes No

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Description: A college professor claims that the entering class this year appears to be smarter than entering classes from previous years. He tests a random sample of 16 of this year's entering students and finds that their mean IQ score is 116, with a standard d

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A college professor claims that the entering class this year appears to be smarter than entering classes from previous years. He tests a random sample of 16 of this year's entering students and finds that their mean IQ score is 116, with a standard deviation of 15. The college records indicate that the mean IQ score for entering students from previous years is 112. If we assume that the IQ scores of this year's entering class are normally distributed, is there enough evidence to conclude, at the 0.05 level of significance, that the mean IQ score, μ, of this year's class is greater than that of previous years?

Perform a one-tailed test and answer questions.

Carry your intermediate computations to at least three decimal places and round your answers.


The null hypothesis:	H0:
The alternative hypothesis:	H1:
The type of test statistic:	(Choose one) Z t Chi square F

The value of the test statistic: (Round to at least three decimal places.)
The critical value at the 0.05 level of significance: (Round to at least three decimal places.)
Can we conclude, using the 0.05 level of significance, that the mean IQ score of this year's class is greater than that of previous years?	Yes	No

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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