For several years researchers have noticed that there appears to be a regular, year-by-year increase in the average IQ for the general population. This phenomenon is called the Flynn effect after the researcher who first reported it (Flynn. 1984, 1999), and it means that psychologists must continuously update IQ tests to keep the population mean at = 100. To evaluate the size of the effect, a researcher obtained a 10-year-old IQ test that was standardized to produce a mean IQ of = 100 for the population 10 years ago. The test was then given to a sample of n = 64 of today's 20-year-old adults. The average score for the sample was M = 107 with a standard deviation of s = 12.
a. Based on the sample, is the average IQ for today's population significantly different from the average 10 years ago, when the test would have produced a mean of = 100? Use a two-tailed test with = .01.
b. Make an 80% confidence interval estimate of today’s population mean IQ for the 10-year-old test.
To state: The decision of hypothesis test performed for the given question using two-tailed test.
The data states that sample size is 64 with the population mean, sample mean, and standard deviation is 100, 107 and 12.
The test hypotheses are:
Null Hypothesis is
Alternative Hypothesis is
Degrees of Freedom:
The critical value is obtained from the t-table for .
The estimated standard error sm:
The t-statistic is obtained as:
Substitute 107 for , 100 for and 1
To make: A 80% confidence interval estimate for the given question
Understanding Basic Statistics
Essentials Of Statistics
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Probability and Statistics for Engineering and the Sciences
Statistics for The Behavioral Sciences (MindTap Course List)
Elements Of Modern Algebra
Calculus: An Applied Approach (MindTap Course List)
Calculus: Early Transcendental Functions (MindTap Course List)
Calculus of a Single Variable
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Single Variable Calculus: Early Transcendentals, Volume I
Trigonometry (MindTap Course List)
Elementary Technical Mathematics
Calculus (MindTap Course List)
Single Variable Calculus
Single Variable Calculus: Early Transcendentals
Finite Mathematics for the Managerial, Life, and Social Sciences
Calculus: Early Transcendentals
Elementary Geometry For College Students, 7e
Mathematical Applications for the Management, Life, and Social Sciences
Precalculus: Mathematics for Calculus (Standalone Book)
Finite Mathematics and Applied Calculus (MindTap Course List)
Calculus: Early Transcendental Functions
Contemporary Mathematics for Business & Consumers
Mathematical Excursions (MindTap Course List)
Introduction To Statistics And Data Analysis
Study Guide for Stewart's Multivariable Calculus, 8th
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Elementary Geometry for College Students