Researchers wished to know if they could conclude that two populations of infant

Question

Researchers wished to know if they could conclude that two populations of infants differ with respect to mean age at which they walked alone. The following data (ages in months) were collected:

Sample from Population A

Sample from Population B

9.5

12.5

10.5

9.5

9.0

13.5

9.75

13.75

10.0

12.0

13.0

13.75

10.0

12.5

13.5

9.5

10.0

12.0

9.5

13.5

10.0

12.0

9.75

12.0

What should the researchers conclude? Let = .05.

a. State the null hypothesis in words and in symbol.

b. State the alternative hypothesis in words and in symbol.

c. Peform independent samples t test using the SPSS. Copy and past the two tables from the output: (1) Group Statistics and (2) Independent Samples Test.

d. Based on the t statistic and p value in output tables, would you reject or retain the null hypothesis? Obtain the critical value using the online software (QuickCalcs GraphPad) and compare t statistic with it. Make sure to enter the right level and the df.

Sample from Population A

Sample from Population B

9.5

12.5

10.5

9.5

9.0

13.5

9.75

13.75

10.0

12.0

13.0

13.75

10.0

12.5

13.5

9.5

10.0

12.0

9.5

13.5

10.0

12.0

9.75

12.0

Explanation / Answer

Solution:

Part a

The null hypothesis for the independent samples t test is given as below:

Null hypothesis: H0: Average ages in months for two populations of infants at which they walked alone are same.

H0: µA = µB

Part b

Alternative hypothesis: Ha: Average ages in months for two populations of infants at which they walked alone are not same.

H0: µA µB

Part c

Required SPSS outputs are given as below:

T-Test

Group Statistics

Population

N

Mean

Std. Deviation

Std. Error Mean

Mean age in months

A

12

10.3750

1.39602

.40300

B

12

12.2083

1.44927

.41837

Independent Samples Test

Levene's Test for Equality of Variances

t-test for Equality of Means

F

Sig.

t

df

Sig. (2-tailed)

Mean Difference

Std. Error Difference

95% Confidence Interval of the Difference

Lower

Upper

Mean age in months

Equal variances assumed

.026

.874

-3.156

22

.005

-1.83333

.58089

-3.03803

-.62863

Equal variances not assumed

-3.156

21.969

.005

-1.83333

.58089

-3.03813

-.62854

Part d

For the given independent samples t test, the p-value is given as 0.005 which is less than = 0.05, so we reject the null hypothesis that Average ages in months for two populations of infants at which they walked alone are same.

For this test, critical value is given as below:

We are given

= 0.05

df = n1 + n2 – 2 = 12 + 12 – 2 = 24 – 2 = 22

Critical value = 2.0739 and -2.0739

(By using t-table or GraphPad)

(There are two critical values because test is two tailed.)

Test statistic = t = -3.156 < lower critical value -2.0739

Test statistic value is out of acceptance region (-2.0739, 2.0739)

So, we reject the null hypothesis H0.

There is insufficient evidence to conclude that Average ages in months for two populations of infants at which they walked alone are same.

There is sufficient evidence to conclude that Average ages in months for two populations of infants at which they walked alone are not same.

Group Statistics

Population

N

Mean

Std. Deviation

Std. Error Mean

Mean age in months

A

12

10.3750

1.39602

.40300

B

12

12.2083

1.44927

.41837

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