# Answer to Question #16785 in Statistics and Probability for sam

Question #16785

The student body at St. Algebra College attends an average of 3.3 parties per month. A random sample of 117 sociology majors averages 3.8 parties per month, with a standard deviation of 0.53. Are sociology majors significantly different from the student body as a whole?

Expert's answer

Build the 95% confidence interval for sociology major’s average number of parties.

Z(1 – (1 – 0.95)/2) = z(0.975) = 1.96

Margin of error:

ME = z * SD / sqrt(n) = 1.96*0.53/sqrt(117) ≈ 0.096

The confidence interval looks:

CI = (P – ME, P + ME) = (3.8 – 0.096, 3.8 + 0.096) ≈ (3.7, 3.9)

The average for all St. Algebra College students, 3.3, is not inside the interval (3.7, 3.9), so under 95% confidence level sociology majors are significantly different from the student body as a whole.

For the 99% confidence level we will get the same result.

Z(1 – (1 – 0.95)/2) = z(0.975) = 1.96

Margin of error:

ME = z * SD / sqrt(n) = 1.96*0.53/sqrt(117) ≈ 0.096

The confidence interval looks:

CI = (P – ME, P + ME) = (3.8 – 0.096, 3.8 + 0.096) ≈ (3.7, 3.9)

The average for all St. Algebra College students, 3.3, is not inside the interval (3.7, 3.9), so under 95% confidence level sociology majors are significantly different from the student body as a whole.

For the 99% confidence level we will get the same result.

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