Answer the following to summarize the test of the hypothesis that there is no dependence between the two variables color vision of participant and trial outcome. For your test, use the 0.05 level of significance. a. Find the value of the test statistic. (Round to two or more decimal places.) b. Find the critical value for a test at the 0.05 level of significance. (Round to two or more decimal places.) c. Can we reject the hypothesis that there is no dependence between the variables color vision of participant and trial outcome? Use the 0.05 level of significance.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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Chapter10: Statistics
Section: Chapter Questions
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Answer the following to summarize the test of the hypothesis that there is no dependence between the two variables color vision of participant and trial outcome. For your test, use the 0.05 level of significance.

a. Find the value of the test statistic. (Round to two or more decimal places.)

b. Find the critical value for a test at the 0.05 level of significance. (Round to two or more decimal places.)

c. Can we reject the hypothesis that there is no dependence between the variables color vision of participant and trial outcome? Use the 0.05 level of significance.  

 

 

uate student performed a visual experiment on a number of participants. Since the experiment involved displays of colored letters and
I
An und
backgrc after the experiment the student wondered whether the presence or absence of color vision in the participants could have produced some of the
effects seen in the data. The student went back, tested his participants for colorblindness, and reanalyzed the data. He considered the variables color vision of
participant ("colorblind" or "not colorblind") and trial outcome ("hit", "miss", "false alarm", or "correct rejection").
The contingency table below gives a summary of the data from 2000 trials of the experiment. Each of the trials was performed either by a colorblind
participant or a non-colorblind participant. Each cell of the table contains three numbers: the first number is the observed cell frequency (f); the second
number is the expected cell frequency (f) under the assumption that there is no dependence between the two variables color vision of participant and trial
outcome; and the third number is the following value.
(fo-ƒE)²
SE
The numbers labeled "Total" are totals for observed frequency.
(Observed cell frequency - Expected cell frequency)²
Expected cell frequency
Transcribed Image Text:uate student performed a visual experiment on a number of participants. Since the experiment involved displays of colored letters and I An und backgrc after the experiment the student wondered whether the presence or absence of color vision in the participants could have produced some of the effects seen in the data. The student went back, tested his participants for colorblindness, and reanalyzed the data. He considered the variables color vision of participant ("colorblind" or "not colorblind") and trial outcome ("hit", "miss", "false alarm", or "correct rejection"). The contingency table below gives a summary of the data from 2000 trials of the experiment. Each of the trials was performed either by a colorblind participant or a non-colorblind participant. Each cell of the table contains three numbers: the first number is the observed cell frequency (f); the second number is the expected cell frequency (f) under the assumption that there is no dependence between the two variables color vision of participant and trial outcome; and the third number is the following value. (fo-ƒE)² SE The numbers labeled "Total" are totals for observed frequency. (Observed cell frequency - Expected cell frequency)² Expected cell frequency
Color vision
of
participant
Colorblind
Not
colorblind
Total
Hit
65
73.54
0.992
649
640.46
0.1
714
Miss
35
30.28
0.736
259
263.72
False alarm
26
31.52
0.967
280
274.48
0.084 0.111]
294
306
Correct
rejection
80
70.66
1.235
606
615.34
0.142
686
Total
206
1794
2000
Transcribed Image Text:Color vision of participant Colorblind Not colorblind Total Hit 65 73.54 0.992 649 640.46 0.1 714 Miss 35 30.28 0.736 259 263.72 False alarm 26 31.52 0.967 280 274.48 0.084 0.111] 294 306 Correct rejection 80 70.66 1.235 606 615.34 0.142 686 Total 206 1794 2000
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