Question

70% of all arrests are young males. Suppose that a random sample of 32 police files showed that 27 were young males. Use a 1% level of significance to test the claim that the population proportion of arrests is different from 70%. (Must Show Work and all 6 steps)

Answer 1

Solution :

Given that ,

1 . H0 : p = 0.70

Ha : p 0.70

2 . This is the two tailed test

= x / n = 27 / 32 = 0.8438

P0 = 70%. = 0.70

1 - P0 = 1 - 0.70 = 0.30

Test statistic = z

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

= 0.8438 - 0.70 / [0.70 ( 1 - 0.70 ) / 32 ]

= 1.774

3 . The test statistic = 1.774

4 . P-value = 0.076

= 0.01

0.0760 > 0.01

P-value >

P - value greater than

5 . Fail to reject the null hypothesis .

6 . There is sufficient evidence to  test the claim that the population proportion of arrests is different from 70%.