The following table shows the Myers-Briggs personalitypreference and area of study for a random sample of 519 collegestudents. In the table, IN refers to introvert, intuitive; ENrefers to extrovert, intuitive; IS refers to introvert, sensing;and ES refers to extrovert, sensing.

Myers-Briggs Preference	Arts &Science	Business	AlliedHealth	RowTotal
IN	63	11	22	96
EN	82	47	25	154
IS	60	40	15	115
ES	74	38	42	154
ColumnTotal	279	136	104	519

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

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: Myers-Briggs type and area of study areindependent.
H₁: Myers-Briggs type and area of study are notindependent.H₀: Myers-Briggs type and area ofstudy are not independent.
H₁: Myers-Briggs type and area of study areindependent.    H₀:Myers-Briggs type and area of study are not independent.
H₁: Myers-Briggs type and area of study are notindependent.H₀: Myers-Briggs type and area ofstudy are independent.
H₁: Myers-Briggs type and area of study areindependent.

(b) 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.)


Are all the expected frequencies greater than 5?

YesNo    

What sampling distribution will you use?

Student'stnormal    chi-squarebinomialuniform

What are the degrees of freedom?


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

p-value > 0.1000.050 < p-value <0.100    0.025 < p-value <0.0500.010 < p-value < 0.0250.005 <p-value < 0.010p-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject orfail to reject the null hypothesis of independence?

Since the P-value > ?, we fail to rejectthe null hypothesis.Since the P-value > ?, wereject the null hypothesis.    Since theP-value ? ?, we reject the null hypothesis.Sincethe P-value ? ?, we fail to reject the nullhypothesis.

(e) Interpret your conclusion in the context of theapplication.

At the 5% level of significance, there is sufficient evidence toconclude that Myers-Briggs type and area of study are notindependent.At the 5% level of significance, there is insufficientevidence to conclude that Myers-Briggs type and area of study arenot independent.