   Chapter 11, Problem 1RE Essentials of Statistics for the B...

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

Solutions

Chapter
Section Essentials of Statistics for the B...

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

Belsky, Weinraub, Owen, and Kelly (2001) reported on the effects of preschool childcare on the development of young children. One result suggests that children who spend more time away from their mothers are more likely to show behavioral problems in kindergarten. Using a standardized scale, the average rating of behavioral problems for kindergarten children is μ = 35. A sample of n = 16 kindergarten children who had spent at .east 20 hours per week in child care during the previous year produced a mean score of M = 42.7 with a standard deviation of s = 6.a. Are the data sufficient to conclude that children with a history of childcare show significantly more behavioral problems than the average kindergarten child? Use a one-tailed test with α = .01.b. Compute the 90% confidence interval for the mean rating of behavioral problems for the population or kindergarten children who have a history of daycare.  с. Write a sentence showing how the outcome of the hypothesis test and the confidence interval would appear in a research report.

a.

To determine
Whether the data sufficient to conclude that children with a history of children show significantly more behavioural problems that the average kindergarten childusing one-tailed test with α=0.01.

Explanation

Given info:

A sample of 16kindergarten children who spent at least 20 hours per week in child care   are selectedfrom a population with mean 35. The sample mean, and standard deviation (s) is found to be 42.7 and 6 respectively. One-tailed hypothesis test using α=0.01 is to be performed.

Calculations:

The null and alternative hypotheses:

The null hypothesis:

H0:μ35

That is, children with a history of children show significantly less behavioural problems that the average kindergarten child.

The alternative hypothesis:

H1:μ>35

That is, children with a history of children show significantly more behavioural problems that the average kindergarten child.

Degrees of freedom:

For a sample size n the degrees of freedom is,

df=n1

Thus, for a sample of n=16 the degrees of freedom is 15.

For a one-tailed test with α=0.01 and df=15, the critical value (CV)  is obtained from the t-table as t=2.602

Test statistic:

t=Mμsm

Calculate sm using the formula:

sm=sn=616=64=1

b.

To determine

To find: Make a 90% confidence interval estimate for the mean rating of behavioural problems for the population of kindergarten children who have a history of day care.

c.

To determine

To write:A sentence that describe how would the outcome of hypothesis test and confidence interval will appear in the research report.

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