Question

One survey conducted by a major leasing company determined that the Lexus is the favorite luxury car for 25% of leases in Atlanta. Suppose a US car manufacturer conducts its own survey in an effort to determine if this figure is correct. Of the 384 leases in Atlanta surveyed, 79 lease a Lexus. Calculate the p-value associated with the test statistic.

0.0228

0.0456

0.1814

0.3628

0.4772

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.25

H_a : p 0.25

= x / n = 79 / 384 = 0.2057

P₀ = 0.25

1 - P₀ = 1 - 0.25 = 0.75

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.2057 - 0.25 / [(0.25 * 0.75) / 384]

Test statistic = z = -2.00

P(z < -2.00) = 0.0228

P-value = 2 * P(z < -2.00)

P-value = 2 * 0.0228

P-value = 0.0456