Question

In the nation of Gondor, the EPA requires that half the new cars sold will meet a certain particulate emission standard a year later. A sample of 64 one-year-old cars revealed that only 24 met the particulate emission standard. The test statistic to see whether the proportion is below the requirement is

Answer 1

Complete Question

In the nation of Gondor, the EPA requires that half the new cars sold will meet a certain particulate emission standard a year later. A sample of 64 one-year-old cars revealed that only 24 met the particulate emission standard. The test statistic to see whether the proportion is below the requirement is:

A -1.645

B -2.066

C -2.000

D-1.960

Answer:

The  correct option is C

Step-by-step explanation:

From the question we are told that

   The  population mean is  $p = 0.50$

    The sample size is  $n = 64$

     The  number that met the standard is  $k = 24$

       

Generally the sample proportion is mathematically evaluated   as

             $\r p = \frac{24}{64}$

             $\r p =0.375$

Generally the standard error is mathematically evaluated as  

       $SE = \sqrt{ \frac{p(1- p )}{n} }$

=>    $SE = \sqrt{ \frac{0.5 (1- 0.5 )}{64} }$

=>   $SE = 0.06525$

The  test statistics is evaluated as

        $t = \frac{ \r p - p }{SE}$

        $t = \frac{ 0.375 - 0.5 }{0.0625}$

        $t = -2$