Question

In January 2020, the unemployment rate in California was currently 3.9%. You guess that the rate specifically in Los Angeles County is higher, since you think that the job market in Los Angeles consists of younger people. You randomly sample 850 employable people in Los Angeles and find that 100 are unemployed. At the 95 percent confidence level, does the data you collected support your claim?

Answer 1

The null and alternative hypothesis

Test statistic

where

100/850 = 0.1176

Thus

=11.84

At 95% confidence , that is 5% level of significance , one tailed critical value of z is 1.65

Since calculated z > 1.65

We reject H0

The data provides sufficient evidence to conclude that unemployment rate at Los Angeles county is significantly higher than 3.9%

Also 95% confidence interval for population proportion of unemployed in Los Angeles county is

= ( 0.096 , 0.139)

= (9.6% , 13.9%)

Since the lower limit of confidence interval is higher than 3.9% , the data provides sufficient evidence to conclude that unemployment rate at Los Angeles county is significantly higher than 3.9%

Note : For 95% confidence , two tailed critical value of z is, zc= 1.96