Math

Instructions: For each question, answer all items. Make sure that you are VERY detailed when you answer the questions. As a rule of thumb, when you are answering any questions using statistics, you should include all statistics in the answer (e.g. if it asks about the mean, put the actual value of the mean in the sentence). Type your answers out underneath each question either bolded or in a different font color (or both). Please do not delete the questions or the output. When you are finished with the assignment, upload it as a .doc, .docx, or .pdf to the assignment on Canvas.

Question 1: Descriptives

a. What is the average writing score? b. What is the standard deviation for social studies scores? c. What is the minimum reading score? d. What is the median math score? e. Write a paragraph describing the distribution of freshman year science scores. Make sure

to include the following statistics: n, mean, median, mode, standard deviation, minimum, maximum, and skewness. Make sure to state whether this is a skewed distribution. While you are writing this as a paragraph, all numbers should be included.

Statistics

reading score writing score math score

social studies

score

freshman yr

science score

N Valid 200 200 200 200 200

Missing 0 0 0 0 0

Mean 52.2300 52.7750 52.4400 52.4050 51.8500

Median 50.0000 54.0000 52.0000 52.0000 53.0000

Mode 47.00 59.00 50.00a 61.00 50.00

Std. Deviation 10.25294 9.47859 9.52207 10.73579 9.90089

Variance 105.123 89.844 90.670 115.257 98.028

Skewness .196 -.482 .280 -.382 -.189

Std. Error of Skewness .172 .172 .172 .172 .172

Range 48.00 36.00 45.00 45.00 48.00

Minimum 28.00 31.00 32.00 26.00 26.00

Maximum 76.00 67.00 77.00 71.00 74.00

Percentiles 25 44.0000 45.2500 45.0000 46.0000 44.0000

50 50.0000 54.0000 52.0000 52.0000 53.0000

75 60.0000 60.0000 59.0000 61.0000 58.0000

a. Multiple modes exist. The smallest value is shown

Question 2: Histogram

a. According to the histogram, what is the mode of this distribution? b. Would you say that this distribution is relatively normal (hint: look at the curve)? c. Does these answers match up with your description of the sample in part e. in

Question 1?

Question 2: One-Sample t-Test

a. What was the dependent variable in this analysis? b. Describe the sample (using n, M, & SD). c. What are the null and alternative hypotheses for this study? d. Write out the t-test formula using the numbers given in the output. Make sure to

write out the original formula in symbols before putting in the numbers from the output.

e. Complete Hypothesis Test Step 4. i. Decision about null hypothesis? ii. Is it signiLicant? iii. Sentence iv. APA style

One-Sample Statistics

N Mean Std. Deviation

Std. Error

Mean

math score 200 52.4400 9.52207 .67331

One-Sample Test

Test Value = 60

t df Sig. (2-tailed)

Mean

Difference

95% Confidence Interval of the

Difference

Lower Upper

math score -11.228 199 .000 -7.56000 -8.8877 -6.2323

Question 3: Related-Samples t-Test

a. What was the dependent variable in this analysis? b. When did they test the students on that dependent variable? c. Describe the sample (using N, M, & SD for each time point). d. What are the null and alternative hypotheses for this study? e. Write out the t-test formula using the numbers given in the output. Make sure to

write out the original formula in symbols before putting in the numbers from the output.

f. Complete Hypothesis Test Step 4. i. Decision about null hypothesis?

Paired Samples Statistics

Mean N Std. Deviation Std. Error Mean

Pair 1 freshman yr science score 51.8500 200 9.90089 .70010

senior yr science score 53.0450 200 12.10145 .85570

Paired Samples Correlations

N Correlation Sig.

Pair 1 freshman yr science score &

senior yr science score

200 .878 .000

Paired Samples Test

Paired Differences

t df

Sig. (2-

tailed)Mean

Std.

Deviati

on

Std.

Error

Mean

95% Confidence

Interval of the

Difference

Lower Upper

Pair

1

freshman yr

science score -

senior yr science

score

-1.19

500

5.8324

1

.41241 -2.00826 -.38174 -2.8

98

199 .004

ii. Is it signiLicant? iii. Sentence iv. APA style

Question 4: Independent-Samples t-Test

a. What was the independent variable in this analysis? b. What was the dependent variable in this analysis? c. Describe both samples (using N, M, & SD for each group). d. What are the null and alternative hypotheses for this study? e. Can you assume equal variances based on Levene’s Test? f. Write out the t-test formula using the numbers given in the output. Make sure to

write out the original formula in symbols before putting in the numbers from the output.

g. Complete Hypothesis Test Step 4. i. Decision about null hypothesis? ii. Is it signiLicant? iii. Sentence iv. APA style

Group Statistics

type of school N Mean Std. Deviation Std. Error Mean

reading score public 168 51.8452 10.42279 .80414

private 32 54.2500 9.19677 1.62578

Independent Samples Test

Levene's Test

for Equality of

Variances t-test for Equality of Means

F Sig. t df

Sig.

(2-

tailed)

Mean

Differe

nce

Std.

Error

Differe

nce

95% Confidence

Interval of the

Difference

Lower Upper

readin

g

score

Equal

variances

assumed

.564 .453 -1.2

17

198 .225 -2.404

76

1.9751

9

-6.299

86

1.490

34

Equal

variances not

assumed

-1.3

26

47.4

96

.191 -2.404

76

1.8137

7

-6.052

60

1.243

08