Question

A car company believes that the percentage of students of a college who owns a vehicle is 60% or less.  A professor disagrees with this, so she conducted a survey of 250 students and found that 166 of them own a vehicle. (a) State the null and alternative hypothesis.

(b) At α=0.025 level, is there enough evidence to support the null hypothesis.

(c) What is the p-value? (read it from the Z-table)

Answer 1

Solution :

a ) This is the left tailed test .

The null and alternative hypothesis is

H0 : p = 0.60

Ha : p < 060

n = 250

x =166

= x / n = 166 / 205 =0.66

P0 = 0.60

1 - P0 = 1 - 0.60 = 0.40

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.66-0.60/ [(0.60*0.40) /250 ]

= 2.06

Test statistic = z = 2.06

P(z < 2.06) = 0.9803

P-value = 0.9803

b ) = 0.025

P-value >

0.9803 > 0.025

c ) Fail to reject the null hypothesis .

There is insufficient evidence to suggest that