30
practice examMultiple Choice

Practice Exam

Question 30 • Statistics

A political pollster claims that 55 percent of voters prefer candidate A. To investigate this claim, a random sample of 75 voters is polled. The pollster finds that 39 of those polled prefer candidate A. He would like to know if the data provide convincing evidence that the true proportion of all voters who prefer candidate A is less than 55 percent What are the values of the test statistic and cap p -value for this test? Use the z -table.

Answer
A
z is equal to the fraction with numerator 0 point 5 2 minus 0 point 5 5 and denominator square root of displaystyle the fraction with numerator 0 point 5 2 times open paren 1 minus 0 point 5 2 close paren and denominator 75 end root comma cap p - value is equal to 0 point 6 0 3 0
B
z is equal to the fraction with numerator 0 point 5 2 minus 0 point 5 5 and denominator square root of displaystyle the fraction with numerator 0 point 5 5 times open paren 1 minus 0 point 5 5 close paren and denominator 75 end root comma cap p - value is equal to 0 point 3 0 1 5
C
z is equal to the fraction with numerator 0 point 5 2 minus 0 point 5 5 and denominator square root of displaystyle the fraction with numerator 0 point 5 5 times open paren 1 minus 0 point 5 5 close paren and denominator 75 end root comma cap p - value is equal to 0 point 6 0 3 0
D
z is equal to the fraction with numerator 0 point 5 2 minus 0 point 5 5 and denominator square root of displaystyle the fraction with numerator 0 point 5 2 times open paren 1 minus 0 point 5 2 close paren and denominator 75 end root comma cap p - value is equal to 0 point 3 0 1 5

Explanation

The sample proportion is 39/75 = 0.52. For a one-proportion z-test, use the claimed proportion, 0.55, to calculate the standard error: √[0.55(1 − 0.55)/75]. This gives z = (0.52 − 0.55)/√[0.55(1 − 0.55)/75] ≈ −0.52. Because the alternative is that the true proportion is less than 0.55, the left-tail p-value is about 0.3015, matching choice B.

AI-written and checked against the verified answer.

Previous
Next