Question

We see that 35 of the 47 compact vehicles have front wheel drive while 38 of the 41 midsize vehicles have front wheel drive. We wish the test that the proportion of front wheel drive cars is the same in compact and midsize vehicles. Formally, we will test H0 : pc = pm vs Ha : pc ̸= pm, where pc and pm are the proportion of front wheel drive cars in compacts and midsize cars. We will test at the 5% significance level. You may assume that the normal approximation is appropriate for these problems cars in compacts and midsize cars. We will test at the 5% significance level. You may assume that the normal approximation is appropriate for these problems.

Answer 1

Here, we have given that,

n1= Number of compact vehicles = 47

x1= Number of compact vehicles have front wheels drive = 35

=Sample proportion of compact vehicles have front wheels drive

=

n2= Number of midsize vehicles = 41

x2= Number of midsize vehicles have front wheels drive = 38

=Sample proportion of midsize vehicles have front wheels drive

=

Claim: To check whether the proportion of front wheel drive cars is the same in compact and midsize vehicles.

The null and alternative hypotheses are as follows:

v/s

Where = The percentage of front wheel drive cars in compact vehicles.

=The percentage of front wheel drive cars in midsize vehicles.

This is the two-tailed test.

Here, we assume that the normal approximation is appropriate for this problem and we are using the two-sample proportion test.

Now, we can find the test statistics

Z-statistics=

                 =

       = -2.41

Now, we can find the p-value

P-value = 2*P( Z-statistics < -2.41) as this is two-tailed test

              = 2* 0.00798

Using standard normal z table see the value corresponding to the z= -2.41

              =0.016

we get the p-value is 0.016

Decision:

Here P-value (0.016) less than (<) 0.05

Conclusion:

we reject the Null hypothesis Ho

we conclude that the proportion of front wheel drive cars is the not same in compact and midsize vehicles.

i.e.There is a significant difference in the proportion of front wheel drive cars in compact and midsize vehicles.