Question

In 1990, 5.8% of job applicants who were tested for drugs failed the test.

A random sample of 1640 current job applicants results in 64 failures (based loosely on

data from the American Management Association).

At the α = 0.01 significance level, test the below claim (i.e., that the failure rate is now

lower)

HO: p = 0.058

HA: p < 0.058

a) Is this an upper tail, lower tail, or two-tail test?

b) Are we testing means or proportions?

c) State the rule of rejection (in terms of p-value and level of significance)

d) Find the p-value

e) Should you reject or not reject HO?

f) Does the result suggest that fewer job applicants now use drugs?

Answer 1

(A) it is a left tailed test as the alternate hypothesis includes less than sign

(B) we are testing for the proportions

(C)significance level is 0.01. Using z critical table for left tailed test at 0.01 level, we get z critical = -2.326

Rejection rule:- Reject Ho if z statistic is less than -2.326

(D) test statistic calculation

using z distribution table to get the p value, we get

p value = 0.0005

(E) Yes, we will reject the null hypothesis because the p value is less than significance level, 0.0005 < 0.01

(F) We have sufficient evidence to conclude that fewer job applicants now use drugs