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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

Research examining the effects of pie school child care has found that children who spent time in day care, especially high-quality day care, perform helter on math and language tests than children who stay home with their mothers (Broberg, Wessels, Lamb, & Hwang, 1997). In a typical study, a researcher obtains a sample of n = 10 children who attended day care before starting school. The children are given a standardized math test for which the population mean is μ = 50. The scores for the sample are as follows; 53, 57, 61, 49, 51, 56, 58, 62, 51, 56.

a. Is this sample sufficient to conclude that the children with a history of preschool day care are significantly different from the general population? Use a two-tailed test with α = .01.

b. Compute Cohen's d to measure the size of the preschool effect.

c. Write a sentence showing how the outcome of the hypothesis lest and the measure of effect size would appear in a research report.

a.

To determine

To check: Whether the children with a history of preschool day-care are significantly different than that of general population using two-tailed test with α=0.01.

Explanation

Given info:

A sample of 10 individual is selected from a population with mean 50. Two-tailed hypothesis test using α=0.01 is to be performed.

Calculations:

The test hypothesis are:

Null Hypothesis is H0:μ=50

 Alternate Hypothesis is H1:μ50

Degrees of Freedom:

df=(n1)=101=9

For a two-tailed test with α=0.01 and df=9, the critical value (CV)  is obtained from the t-table as t=±3.250

The t-statistics is obtained by,

t=Mμsm

Software procedure:

Step-by-step procedure to obtain the sample mean and standard error, sm using the SPSS software:

  • Go to Variable View> Enter the name of the variable as Sample.
  • Go to Data View>Enter the values of Samples.
  • Choose Analyze > Descriptive Statistics> choose Descriptive

b.

To determine

To find: The Cohen’s d.

c.

To determine

To State:  The outcome of hypothesis test and measure of effect size will appear in the research report.

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