Question

According to a national statistics bureau, in 2000, 21.8% of males living in the Southwest were retired exterminators. A researcher believes that the percentage has increased since then. She randomly selects 275 males in the Southwest and finds that 68 of them are retired exterminators. Test this researcher's claim at the 2% level of significance.(Round to two decimal places)

(a) Critical Value:

(b) Test Score

(c) Construct a 98% confidence interval for the proportion of retired exterminators. (Round to 2 decimal places)

Answer 1

a) As we are testing here whether the proportion has increased from 21.8%, therefore the null and the alternative hypothesis here are given as:

From standard normal tables, we have:
P(Z < 2.054) = 0.98.

Therefore, P(Z > 2.054) = 1- 0.98 = 0.02

Therefore 2.054 is the required critical value here.

b) The sample proportion is computed here as:
p = x/n = 68/275 = 0.2473

The test statistic here is computed as:

Therefore 1.1768 is the required test statistic value here.

c) From standard normal tables, we have:
P(Z < 2.326) = 0.99

Therefore, due to symmetry, we get here:
P( - 2.326 < Z < 2.326) = 0.98

Therefore the confidence interval here is obtained as:

This is the required confidence interval here.