Morgan City Fire Chief Sidney Pyro is concerned about the low efficiency scores that his firefighters receive at the state testing institute. Chief Pyro believes that these scores result because some firefighters are not in good physical condition. Pyro orders 75 randomly selected firefighters to participate in an hour of exercise per day. Another 200 firefighters have no required exercise. After 60 days, all firefighters are tested again by the state. Chief Pyro collects the data and performs a two-sample independent t-test by using SPSS to examine if there is a statistically significant difference between the treatment and control groups; the SPSS results are shown in the table below. Group Statistics Groups N Mean Std. Deviation Std. Error Mean Test Scores Treatment 75 74.5 31.4 3.6 Control 200 70.6 26.3 1.9 a. Formulate a null and research hypothesis: H0: H1: Collect all the necessary data: Mean score of the treatment group: Mean score of the control group: Sample size of the treatment group: Sample size of the control group: Standard deviation of the treatment group: Standard deviation of the control group: Decide which test to use. Determine the level of significance. Independent Sample Test Levene's Test for Equality of Variance t-test for Equality of Means F Sig. t df Sig. Mean Difference Test Scores Equal variances assumed .0248 .6723 .9582 273 .3047 3.9 Equal variances not assumed .9208 257.23 .3037 3.9 Based on the results of Levene’s test, find the proper t test statistic and the p-value. Compare the test statistic to the critical value, and compare the p-value to the alpha level (level of significance). Reject, or do not reject, the null hypothesis. What is your conclusion?
Morgan City Fire Chief Sidney Pyro is concerned about the low efficiency scores that his firefighters receive at the state testing institute. Chief Pyro believes that these scores result because some firefighters are not in good physical condition. Pyro orders 75 randomly selected firefighters to participate in an hour of exercise per day. Another 200 firefighters have no required exercise. After 60 days, all firefighters are tested again by the state. Chief Pyro collects the data and performs a two-sample independent t-test by using SPSS to examine if there is a statistically significant difference between the treatment and control groups; the SPSS results are shown in the table below.
Group Statistics
|
Groups |
N |
Mean |
Std. Deviation |
Std. Error Mean |
|
|
Test Scores |
Treatment |
75 |
74.5 |
31.4 |
3.6 |
|
|
Control |
200 |
70.6 |
26.3 |
1.9 |
a. Formulate a null and research hypothesis:
-
- H0:
- H1:
- Collect all the necessary data:
- Mean score of the treatment group:
- Mean score of the control group:
Sample size of the treatment group:- Sample size of the control group:
- Standard deviation of the treatment group:
- Standard deviation of the control group:
- Decide which test to use.
- Determine the level of significance.
Independent Sample Test
|
|
|
Levene's Test for Equality of Variance |
t-test for Equality of Means |
||||
|
|
|
F |
Sig. |
t |
df |
Sig. |
Mean Difference |
|
Test Scores |
Equal variances assumed |
.0248 |
.6723 |
.9582 |
273 |
.3047 |
3.9 |
|
|
Equal variances not assumed |
|
|
.9208 |
257.23 |
.3037 |
3.9 |
Based on the results of Levene’s test, find the proper t test statistic and the p-value.
Compare the test statistic to the critical value, and compare the p-value to the alpha level (level of significance).
Reject, or do not reject, the null hypothesis.
What is your conclusion?
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