Thanks to an initiative to recruit top students, an administrator at a college claims that this year's entering class must have a greater mean IQ score than that of entering classes from previous years. The administrator tests a random sample of 14 of this year's entering students and finds that their mean IQ score is 114 , with a standard deviation of 13 . The college records indicate that the mean IQ score for entering students from previous years is 111 . Is there enough evidence to conclude, at the 0.05 level of significance, that the population mean IQ score, μ , of this year's class is greater than that of previous years? To answer, assume that the IQ scores of this year's entering class are approximately normally distributed. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H0 and the alternative hypothesis H1 . H0: H1: (b) Determine the type of test statistic to use. ▼(Choose one) (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 that the mean IQ score of this year's class is greater than that of previous years? Yes No

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 7PPS

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Question

Thanks to an initiative to recruit top students, an administrator at a college claims that this year's entering class must have a greater mean IQ score than that of entering classes from previous years. The administrator tests a random sample of

of this year's entering students and finds that their mean IQ score is

114

, with a standard deviation of

. The college records indicate that the mean IQ score for entering students from previous years is

111

Is there enough evidence to conclude, at the

0.05

level of significance, that the population mean IQ score,

, of this year's class is greater than that of previous years? To answer, assume that the IQ scores of this year's entering class are approximately normally distributed.

Perform a one-tailed test. Then complete the parts below.

Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)

(a)	State the null hypothesis H0 and the alternative hypothesis H1 .
H0:
H1:
(b)	Determine the type of test statistic to use.
	▼(Choose one)
(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 that the mean IQ score of this year's class is greater than that of previous years?
Yes No

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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