Question 1 (15 marks)

a) Use the variable "Age" to construct the confidence intervals for the estimate of population mean. Find the confidence interval for "Age" with "training level" (Code=A), at both 92% and 96% levels. Interpret your confidence intervals.

b) Did you make any assumptions when constructing your confidence intervals? If yes, which assumptions; if not, why?

Data:

T-TEST GROUPS=Training.level('A' 'B')

/MISSING=ANALYSIS

/VARIABLES=Age

/ES DISPLAY(FALSE)

/CRITERIA=CI(.92).

T-Test

Notes

Output Created

10-APR-2021 23:43:34

Comments

Input

Data

C:\Users\ata.yilmaz\Desktop\CQMS202Group_81.csv

Active Dataset

DataSet1

Filter

Weight

Split File

N of Rows in Working Data File

60

Missing Value Handling

Definition of Missing

User defined missing values are treated as missing.

Cases Used

Statistics for each analysis are based on the cases with no missing or out-of-range data for any variable in the analysis.

Syntax

T-TEST GROUPS=Training.level('A' 'B')

/MISSING=ANALYSIS

/VARIABLES=Age

/ES DISPLAY(FALSE)

/CRITERIA=CI(.92).

Resources

Processor Time

00:00:00.00

Elapsed Time

00:00:00.00

Group Statistics

Training.level

N

Mean

Std. Deviation

Std. Error Mean

Age

A

32

46.22

7.294

1.289

B

20

45.15

7.506

1.678

Independent Samples Test

Levene's Test for Equality of Variances

t-test for Equality of Means

F

Sig.

t

df

Age

Equal variances assumed

.017

.896

.508

50

Equal variances not assumed

.505

39.593

Independent Samples Test

t-test for Equality of Means

Sig. (2-tailed)

Mean Difference

Std. Error Difference

92% Confidence Interval of the Difference

Lower

Age

Equal variances assumed

.613

1.069

2.102

-2.688

Equal variances not assumed

.616

1.069

2.117

-2.734

Independent Samples Test

t-test for Equality of Means

92% Confidence Interval of the Difference

Upper

Age

Equal variances assumed

4.826

Equal variances not assumed

4.872

T-TEST GROUPS=Training.level('A' 'B')

/MISSING=ANALYSIS

/VARIABLES=Age

/ES DISPLAY(FALSE)

/CRITERIA=CI(.96).

T-Test

Notes

Output Created

10-APR-2021 23:44:00

Comments

Input

Data

C:\Users\ata.yilmaz\Desktop\CQMS202Group_81.csv

Active Dataset

DataSet1

Filter

Weight

Split File

N of Rows in Working Data File

60

Missing Value Handling

Definition of Missing

User defined missing values are treated as missing.

Cases Used

Statistics for each analysis are based on the cases with no missing or out-of-range data for any variable in the analysis.

Syntax

T-TEST GROUPS=Training.level('A' 'B')

/MISSING=ANALYSIS

/VARIABLES=Age

/ES DISPLAY(FALSE)

/CRITERIA=CI(.96).

Resources

Processor Time

00:00:00.00

Elapsed Time

00:00:00.00

Group Statistics

Training.level

N

Mean

Std. Deviation

Std. Error Mean

Age

A

32

46.22

7.294

1.289

B

20

45.15

7.506

1.678

Independent Samples Test

Levene's Test for Equality of Variances

t-test for Equality of Means

F

Sig.

t

df

Age

Equal variances assumed

.017

.896

.508

50

Equal variances not assumed

.505

39.593

Independent Samples Test

t-test for Equality of Means

Sig. (2-tailed)

Mean Difference

Std. Error Difference

96% Confidence Interval of the Difference

Lower

Age

Equal variances assumed

.613

1.069

2.102

-3.365

Equal variances not assumed

.616

1.069

2.117

-3.426

Independent Samples Test

t-test for Equality of Means

96% Confidence Interval of the Difference

Upper

Age

Equal variances assumed

5.502

Equal variances not assumed

5.564

T-TEST

/TESTVAL=0

/MISSING=ANALYSIS

/VARIABLES=Age

/ES DISPLAY(TRUE)

/CRITERIA=CI(.95).

T-Test

Notes

Output Created

10-APR-2021 23:45:09

Comments

Input

Data

C:\Users\ata.yilmaz\Desktop\CQMS202Group_81.csv

Active Dataset

DataSet1

Filter

Weight

Split File

N of Rows in Working Data File

60

Missing Value Handling

Definition of Missing

User defined missing values are treated as missing.

Cases Used

Statistics for each analysis are based on the cases with no missing or out-of-range data for any variable in the analysis.

Syntax

T-TEST

/TESTVAL=0

/MISSING=ANALYSIS

/VARIABLES=Age

/ES DISPLAY(TRUE)

/CRITERIA=CI(.95).

Resources

Processor Time

00:00:00.00

Elapsed Time

00:00:00.00

One-Sample Statistics

N

Mean

Std. Deviation

Std. Error Mean

Age

60

45.58

7.155

.924

One-Sample Test

Test Value = 0

t

df

Sig. (2-tailed)

Mean Difference

95% Confidence Interval of the Difference

Lower

Upper

Age

49.347

59

.000

45.583

43.73

47.43

One-Sample Effect Sizes

Standardizer^a

Point Estimate

95% Confidence Interval

Lower

Upper

Age

Cohen's d

7.155

6.371

5.194

7.542

Hedges' correction

7.248

6.289

5.128

7.446

a. The denominator used in estimating the effect sizes.

Cohen's d uses the sample standard deviation.

Hedges' correction uses the sample standard deviation, plus a correction factor.