Assume that you work in a market research department You are

Assume that you work in a market research department. You are asked to write a report about a claim that 47% of all new car buyers prefer a four-door car. Discuss how you could use a random sample to test this hypothesis. State the null and alternate hypothesis using the proper notation. State the formula for calculating the standardized sample test statistic, z. How will you decide if you should reject or accept the null hypothesis?

Solution

Using a random sample large enough (say, around 1000), we ask them as to whether they prefer a four-door car or not.

Then we test the hypotheses

Ho: p = 0.47
Ha: p =/= 0.47

at a certain significance level, say 0.05. We test it using the sample statistic we got, p^.

We will use the formula
          
p^ = x / n      
          
and get the standard error of p^, sp,          
          
sp = sqrt[po (1 - po)/n]

where po = the hypothesized proportion = 0.47.
          
We get the z statistic using
          
z = (p^ - po)/sp
          
We can use the critical value for z (reject Ho if |z| > 1.96 if alpha = 0.05) or get its P value and reject ho if P < 0.05.