Question

One attorney claims that more than 25% of all the lawyers in Boston advertise for their business. A sample of 200 lawyers in Boston showed that 63 of the lawyers had used some form of advertising for their business. At ???? =0.05, is there enough evidence to support the attorney’s claim? (Use the P-value method to test this hypothesis)

Answer 1

There is enough evidence to support the attorney’s claim

Explanation:

Given that one attorney claims that more than 25% of all the lawyers in Boston advertise for their business.

Sample size n =200

Sample proportion =
`63/200=0.315`

Hypotheses:

`H_0: p=0.25\\H_a: p>0.25`

(right tailed testat 5% significance level)

Assuming H0 to be true, std error of p =
`\sqrt{0.25*0.75/200 \\=0.0306`

Test statistic z = p diff/std error

=
`(0.315-0.25)/(0.0306) \\=2.12`

p value for one tailed =0.0170

Since p <0.05 we reject null hypothesis

There is enough evidence to support the attorney’s claim