The following table shows the Myers-Briggs personality preference and area of study for a random sample of 519 college students. In the table, IN refers to introvert, intuitive; EN refers to extrovert, intuitive; IS refers to introvert, sensing; and ES refers to extrovert, sensing. Myers-Briggs Preference Arts & Science Business Allied Health Row Total IN 59 11 26 96 EN 86 37 31 154 IS 53 39 23 115 ES 77 42 35 154 Column Total 275 129 115 519 Use a chi-square test to determine if Myers-Briggs preference type is independent of area of study at the 0.05 level of significance.  Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.) What are the degrees of freedom?  Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.) p-value > 0.100 0.050 < p-value < 0.100  0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.005 < p-value < 0.010 p-value < 0.005   Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence? Since the P-value > α, we fail to reject the null hypothesis. Since the P-value > α, we reject the null hypothesis.     Since the P-value ≤ α, we reject the null hypothesis. Since the P-value ≤ α, we fail to reject the null hypothesis.   Interpret your conclusion in the context of the application. At the 5% level of significance, there is sufficient evidence to conclude that Myers-Briggs type and area of study are not independent. At the 5% level of significance, there is insufficient evidence to conclude that Myers-Briggs type and area of study are not independent.

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The following table shows the Myers-Briggs personality preference and area of study for a random sample of 519 college students. In the table, IN refers to introvert, intuitive; EN refers to extrovert, intuitive; IS refers to introvert, sensing; and ES refers to extrovert, sensing.

Myers-Briggs
Preference
Arts & Science Business Allied Health Row Total
IN 59 11 26 96
EN 86 37 31 154
IS 53 39 23 115
ES 77 42 35 154
Column Total 275 129 115 519

Use a chi-square test to determine if Myers-Briggs preference type is independent of area of study at the 0.05 level of significance.

 Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)

What are the degrees of freedom?

 Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

p-value > 0.100
0.050 < p-value < 0.100 
0.025 < p-value < 0.050
0.010 < p-value < 0.025
0.005 < p-value < 0.010
p-value < 0.005
 
Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?
Since the P-value > α, we fail to reject the null hypothesis.
Since the P-value > α, we reject the null hypothesis.    
Since the P-value ≤ α, we reject the null hypothesis.
Since the P-value ≤ α, we fail to reject the null hypothesis.
 
Interpret your conclusion in the context of the application.
At the 5% level of significance, there is sufficient evidence to conclude that Myers-Briggs type and area of study are not independent.
At the 5% level of significance, there is insufficient evidence to conclude that Myers-Briggs type and area of study are not independent.    
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