Question

ate DMV records indicate that of all vehicles undergoing emissions testing during the previous year, 70% passed on the first try. A random sample of 203 cars tested in a particular county during the current year yields 115 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 = .05. (a) Choose the appropriate hypotheses. OH : p= 0.70 versus H, :p > 0.70 OH : p= 0.70 versus Hip < 0.70 . H :p= 0.70 versus H, :p +0.70 OH : p< 0.70 versus H, :p=0.70 OH :p> 0.70 versus H, :p=0.70 (b) What is the value of the test statistic for this test? (c) What is the critical value for this test? + (d) State your conclusions. Reject the null hypothesis, there is a significant difference in proportions. Reject the null hypothesis, there is not a significant difference in proportions. O Fail to reject the null hypothesis, there is not a significant difference in proportions. Fail to reject the null hypothesis, there is a significant difference in proportions.

Answer 1

Answer:

n= 203, x= 115, P = 70% = 0.70, $//img.homeworklib.com/questions/aa01dcd0-9ff5-11eb-9a5b-2bcd2556fbd0.png?x-oss-process=image/resize,w_560$ = 0.05

$\hat p = \frac{x}{n} = \frac{115}{203} = 0.567$

a)

The null and alternative hypothesis is

Ho: P = 0.70

H1: P  $\neq$ 0.70

formula for test statistics is

-P p*(1-P) n

0.567 – 0.70 0.7+(1-0.7) 203

test statistics: z = - 4.15

b)

now calculate z critical value for two tailed test with $//img.homeworklib.com/questions/aa01dcd0-9ff5-11eb-9a5b-2bcd2556fbd0.png?x-oss-process=image/resize,w_560$ = 0.05

we get,

Critical value = $\pm$ 1.96

decision rule is

Reject Ho if ( test statistics ) < -1.96 or if ( test statistics ) > 1.96

here, ( test statistics = -4.15  ) < ( -1.96 )

Hence, we can say,

Reject the null hypothesis, there is a significant difference in proportions.