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Two Sample T test for testing the Hypothesis of Means

An experiment was conducted to compare mean reaction time to 2 types of traffic signs, prohibitive (No Left Turn) and permissive (Left Turn Only). Ten subjects were included in the experiment. Each subject was presented with 40traffice signs: 10 prohibitive and 10 permissive in random order. The mean time to reaction and the number of correct actions were recorded for each subject. The mean reaction times to both are listed below:

Table Mean Reaction Times for 20 Traffic Signs
Prohibitive Permissive
1 824 737
2 866 585
3 841 718
4 770 723
5 829 675
6 764 711
7 857 626
8 831 697
9 846 730
10 759 739

a. Explain why or why not this study is a paired-difference design. Provide reasons why pairing or independent samples should be useful in increasing information regarding the difference between the mean reaction times to prohibitive and permissive traffic signs.

b. Determine if the there is sufficient evidence to indicate a difference in the mean reaction times of prohibitive and permissive traffic signs.

1. What are the null and alternative hypotheses?

2. What is the level of significance?

3. Test the null hypothesis, what can you conclude? (Be sure to include the test statistic, critical value, p-value and an interpretive statement)

4. What are 2 plausible alternative explanations for the results?

5. What are the implications of the results (include a course of action)?

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