# A standardized math test was a

A standardized math test was administered to two groups of 5th graders, one group sampled from classes whose teachers had followed the existing curriculum and one group sampled from classes whose teachers had followed a new curriculum, and the scores were compared using a t-test with the following results:  Old Curriculum           New Curriculum

Mean                    75.31914894               65.65957447

Variance                118.613321                 801.1424607

Observations                         47                                47

Pooled Variance     459.8778908

Hypothesized Mean Difference  0

df                                           92

t Stat                        2.1835887807

P(T<=)one tail          0.015768226

t Critical one-tail       1.661585397

P(T<=t) two-tail         0.031536452

t Critical two-tail         1.986086317

You decide to use the conventional p=.05 as your cutoff for statistical significance.  What do you conclude from this analysis?

a.  The wrong t-test was conducted because of the relative sizes of the two groups’ variances.

b.  We cannot be sufficiently confident that there is a relationship between the math curriculum followed and students’ test scores.

# A standardized math test was a

A standardized math test was administered to two groups of 5th graders, one group sampled from classes whose teachers had followed the existing curriculum and one group sampled from classes whose teachers had followed a new curriculum, and the scores were compared using a t-test with the following results:   Old Curriculum               New Curriculum

Mean                                65.06382979                    66.5106383

Variance                           822.4523589                    127.5161887

Obervations                                      47                                    47

Hypothesized Mean Difference          0

df                                                      60

t Stat                               -0.321814324

P(T<=t)                                          0.37

t Critical one-tail              1.670648865

P(T<=t) two-tail                             0.75

t Critical two-tail               2.000297822

You decide to use the conventional p=.05 as your cutoff for statistical significance.  What do you conclude from this analysis?

a.  The wrong t-test was conducted because of the relative sizes of the two groups’ variances.

b.  We should reject the null hypothesis, which is that the two groups’ means are equal in the populaton of 5th graders.

c.  We should not reject the null hypothesis, which is that the two groups’ means are equal in the population of 5th graders.

d.  We should reject the null hypothesis, which is that the two groups’means are not equal in the population of 5th graders.

# A standardized math test was a

A standardized math test was administered to two groups of 5th graders, one group sampled from classes whose teachers had followed the existing curriculum and one group sampled from classes whose teachers had followed a new curriculum, and the scores were compared using a t-test with the following results:   Old Curriculum               New Curriculum

Mean                                75.31914894                    75.4893617

Variance                           118.613321                       33.8640148

Obervations                                      47                                    47

Hypothesized Mean Difference          0

df                                                      70

t Stat                               -0.094501437

P(T<=t)                                          0.46

t Critical one-tail              1.666914479

P(T<=t) two-tail                             0.92

t Critical two-tail               1.994437112

You decide to use the conventional p=.05 as your cutoff for statistical significance.  What do you conclude from this analysis?

a.  The wrong t-test was conducted because of the relative sizes of the two groups’ variances.

b.  We should reject the null hypothesis, which is that the two groups’ means are equal in the population of 5th graders.

c.  We should not reject the null hypothesis, which is that the two groups’ means are equal in the population of 5th graders.

d.  We should reject the null hypothesis, which is that the two groups’ means are not equal in the population of 5th graders.

e.  We should not reject the null hypothesis, which is that the two groups’ means are not equal in the population of 5th graders.

# A standardized math test was a

A standardized math test was administered to two groups of 5th graders, one group sampled from classes whose teachers had followed the existing curriculum and one group sampled from classes whose teachers had followed a new curriculum, and the scores were compared using a t-test with the following results:   Old Curriculum               New Curriculum

Mean                                68.76595745                    75.4893617

Variance                           22.226642                         33.8640148

Obervations                                      47                                    47

Hypothesized Mean Difference          0

df                                                      88

t Stat                               -6.154501628

P(T<=t)                                          0.00

t Critical one-tail              1.662354029

P(T<=t) two-tail                             0.00

t Critical two-tail               1.987289865

You decide to use the conventional p=.05 as your cutoff for statistical significance.  What do you conclude from this analysis?

a.  The wrong t-test was conducted because of the relative sizes of the two groups’ variances.

b.  We should reject the null hypothesis, which is that the two groups’ means are equal in the population of 5th graders.

c.  We should not reject the null hypothesis, which is that the two groups’ means are equal in the population of 5th graders.

d.  We should reject the null hypothesis, which is that the two groups’ means are not equal in the population of 5th graders.

e.  We should not reject the null hypothesis, which is that the two groups’ means are not equal in the population of 5th graders.

# A standardized math test was a

A standardized math test was administered to two groups of 5th graders, one group sampled from classes whose teachers had followed the existing curriculum and one group sampled from classes whose teachers had followed a new curriculum, and the scores were compared using a t-test with the following results:   t-test: Two-Sample Assuming Equal Variances

Old Curriculum               New Curriculum

Mean                                75.31914894                    65.65957447

Variance                           118.613321                       801.1424607

Obervations                                      47                                    47

Hypothesized Mean Difference          0

df                                                      92

t Stat                               2.183587807

P(T<=t) one-tail              0.015768226

t Critical one-tail              1.661585397

P(T<=t) two-tail               0.031536452

t Critical two-tail               1.986086317

You decide to use the conventional p=.05 as your cutoff for statistical significance.  What do you conclude from this analysis?

1. The wrong t-test was conducted because of the relative sizes of the two groups’ variances.
2. We cannot be sufficiently confident that there is a relationship between the math curriculum followed and students’ test scores.
3. There probably is a relationship between the math curriculum followed and students’ test scores.

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