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 14 of this year's entering students and finds that their mean IQ score is 118 , with standard deviation of 10 . The college records indicate that the mean IQ score for entering students from previous years is 115. 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. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (a) State the null hypothesis H0 ? and the alternative hypothesis H1? . H0: H1: (b) Determine the type of test statistic to use. ▼(Choose one) z t chi square or f ? (c) Find the value of the test statistic?. (Round to three or more decimal places.) (d) Find the p-value.? (Round to three or more decimal places.) (e) 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 or 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 14 of this year's entering students and finds that their mean IQ score is 118 , with standard de

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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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 14 of this year's entering students and finds that their mean IQ score is 118 , with standard deviation of 10 . The college records indicate that the mean IQ score for entering students from previous years is 115. 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. Then complete the parts below.

Carry your intermediate computations to three or more decimal places and round your answers as specified in the table.

(a)	State the null hypothesis H0 ? and the alternative hypothesis H1? .
H0:
H1:
(b)	Determine the type of test statistic to use.
	▼(Choose one) z t chi square or f ?
(c)	Find the value of the test statistic?. (Round to three or more decimal places.)

(d)	Find the p-value.? (Round to three or more decimal places.)

(e)	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 or 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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Solution:

Let X be the IQ score.

From the given information, x-bar = 118, S=10 and n=14.

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