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TESTING HYPOTHESISTESTING HYPOTHESISABOUT ONE SAMPLEABOUT ONE SAMPLE

MEANMEANDR. ALICE D. DIOQUINO

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Three objectives of the researcherThree objectives of the researcher

y To test whether the sample mean is

greater than the hypothesized populationvalue.

y To test whether the sample mean is lessthan the hypothesized population value.

y To test whether the sample mean is notequal to the hypothesized populationvalue.

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yObjectives 1 and 2 are

associated with directional orone-tailed tests.

yObjective 3 is associated with a

non-directional or two-tailedtest.

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Sample Research ProblemSample Research ProblemThe increase in the number of children who are

schooled at home has stimulated numerous researchquestions regarding the characteristics of thesechildren. One such question is related to their level of intelligence. Do home-schooled children possess thesame average level of intelligence as other children?

It might be assumed that parents who decide toeducate their children at home are fairly bright, andthat their children in turn, are also fairly bright. Aresearcher who was interested in this questionrandomly selected 12 seven-year-olds who were beinghome-schooled and administered to each child the

Wechsler Intelligence Scale for Children (WISC). Thepublished norms for the WISC indicate that the scoresfor the population are normally distributed with amean equal to 100 and sd equal to 15.

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Research QuestionResearch Question

y Is the mean score on the WISC for seven-

year-old home-schooled significantlydifferent from the population mean of 100?

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HYPOTHESeSHYPOTHESeS

y H0 = There is no significant difference in

the mean score of the sample to thepopulation mean.

y H1= The mean score for home-schooledchildren is less than 100.

y H2= The mean score for home-schooledchildren is greater than 100.

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ASSUMPTIONS UNDERLYING THEASSUMPTIONS UNDERLYING THEZZ--TESTTEST

y Observations are independent of one

another.y The observations are randomly sampled

from the population

y Observations are normally distributed

from the populationy The population variance, 2, is known

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INTERPRETING THE OUTPUTINTERPRETING THE OUTPUT

ONE-SAMPLE Z TEST

Sample Mean 106.0833

Hypothesized population mean 100

population standard deviation 15

Count 12

Standard Error of the mean 4.330127

Z 1.404886

Alpha 0.05

Probability one-tailed 0.080028

Z critical one-tailed 1.644854

Probability two-tailed 0.160055

Z critical two-tailed 1.959964

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CONCLUSIONSCONCLUSIONS

y The one-tailed test is not statistically

significant because the obtained Z(1.404886) is not greater than the criticalZ (1.644853)

y The two-tailed test is not also statistically

significant because obtained Z (1.404886)is less than the critical Z (1.959961)

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y ACCEPT H0 that there is no significant

difference in the WISC mean score of theseven-year-olds in this study to thepopulation mean.