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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

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 μ = 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 μ = 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 μ = 100? Use a two-tailed test with α = .01.

b. Make an 80% confidence interval estimate of today’s population mean IQ for the 10-year-old test.

a.

To determine

To state: The decision of hypothesis test performed for the given question using two-tailed test.

Explanation

Given info:

The data states that sample size is 64 with the population mean, sample mean, and standard deviation is 100, 107 and 12.

Calculations:

The test hypotheses are:

Null Hypothesis is H0:μ=100

Alternative Hypothesis is H1:μ100

Degrees of Freedom:

df=n1=641=63

The critical value is obtained from the t-table for tα=0.01(63)=±2.

The estimated standard error sm:

sm=sn=1264=1.5

The t-statistic is obtained as:

t=Mμsm

Substitute 107 for M, 100 for μ and 1

b.

To determine

To make: A 80% confidence interval estimate for the given question

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