Are most student government leaders extroverts? According to Myers-Briggs estimates, about 82% of college student government leaders are extroverts.Suppose that a Myers-Briggs personality preference test was given to a random sample of74student government leaders attending a large national leadership conference and that54were found to be extroverts. Does this indicate that the population proportion of extroverts among college student government leaders is different (either way) from 82%? Use= 0.01.

(a) What is the level of significance?

(b) State the null and alternate hypotheses.

• H₀:p= 0.82;H₁:p> 0.82
• H₀:p= 0.82;H₁:p0.82
• H₀:p> 0.82;H₁:p= 0.82
• H₀:p0.82;H₁:p= 0.82
• H₀:p= 0.82;H₁:p< 0.82

(c) What sampling distribution will you use?

• 1. The standard normal, sincenp< 5 andnq< 5.
• 2. The Student'st, sincenp< 5 andnq< 5.
• 3. The Student'st, sincenp> 5 andnq> 5.
• 4. The standard normal, sincenp> 5 andnq> 5.

(d) What is the value of the sample test statistic? (Round your answer to two decimal places.)

(e) Find theP-value of the test statistic. (Round your answer to four decimal places.)

(f) Sketch the sampling distribution and show the area corresponding to theP-value.

(g) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level?

• 1. At the= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.
• 2. At the= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.
• 3. At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
• 4. At the= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(h) Interpret your conclusion in the context of the application.

• 1. There is sufficient evidence at the 0.01 level to conclude that the true proportion of extroverts among college student government leaders differs from 82%.
• 2. There is insufficient evidence at the 0.01 level to conclude that the true proportion of extroverts among college student government leaders differs from 82%.