Question

A research center claims that more than 29% of US employees have changed jobs in the past three years. In a random sample of 180 US employees, 63 have changed jobs in the past three years. At a=0.10, is there enough evidence to reject the null hypothesis?          Ho: p <= 0.29 Ha: p>0.29.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p 0.29

Ha : p > 0.29

= x / n = 63 / 180 = 0.35

P0 = 0.29

1 - P0 = 1 - 0.29 = 0.71

Test statistic = z

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

= 0.35 - 0.29/ [(0.29 * 0.71) / 180 ]

Test statistic = z = 1.77

P(z > 1.77 ) = 1 - P(z < 1.77) = 1 - 0.9616

P-value = 0.0384

= 0.10   

P-value <

Reject the null hypothesis .

There is sufficient evidence to suggest that more than 29% of US employees have changed jobs in the past three years