Question

A publisher reports that 42% of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 370 found that 38% of the readers owned a particular make of car. Make the decision to reject or fail to reject the null hypothesis at the 0.02 level.

Answer 1

Type I and type II errors

Explanation:

We perform our error parameter defining that our null hypothesis H0 is determined for all that percentage that is not 42%, while the null hypothesis H1 is determined by the values that are 42%, that is

H0: p is not 42% vs H1: p = 42%

We proceed to obtain the standard deviation with the data we have and perform the calculation of error by proportions,

The standard deviation is:

`\sigma = √(p*(1-p)/n)`

Where p is our proportion,

`\sigma = √((0.42*(1-0.42))/370) = 0.025689`

Z -score is

`z= (p-P)/(\sigma)`

where P is the Random Sample,

(p-P)/σ =
`z= (0.42-0.38)/(0.025689)  = 1.557`

CONCLUSION:

There is statistical evidence that the proportions are different. H0 is accepted.