State DMV records indicate that of all vehicles undergoing emissions testing during the previous year, 70% passed on the first try. A random sample of 200 cars tested in a particular county during the current year yields 124 that passed on the initial test. Does this suggest that the true proportion for this county during the current year differs from the previous statewide proportion? Test the relevant hypotheses using a ¼ .05.

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windyyork windyyork · Answer 1 · 2019-11-26T07:27:14+01:00

Answer: Yes , this suggests that the true proportion for this country during the current year differs from the previous statewide proportion.

Step-by-step explanation:

Since we have given that

Sample size n = 200

Hypothesis:

[tex]H_0:p=0.7\\\\H_a:p\neq 0.7[/tex]

Number of cars that passed on the initial test = 124

So, [tex]\hat{p}=\dfrac{124}{200}=0.62[/tex]

At α = 0.05 level of significance.

So, z = 1.96 (critical value)

Now, we will find the test statistic value.

[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\z=\dfrac{0.62-0.7}{\sqrt{\dfrac{0.7\times 0.3}{200}}}\\z=\dfrac{-0.08}{0.032}\\\\z=-2.5[/tex]

Since -2.5<1.96.

So, we will reject the null hypothesis.

Hence, Yes , this suggests that the true proportion for this country during the current year differs from the previous statewide proportion.