12. The police department of Youbet, Michigan, is considering the purchase of ne

Question

12. The police department of Youbet, Michigan, is considering the purchase of new radar guns. On the average, the guns presently used by the department can detect a speeding vehicle at a distance of 2217 feet. In order to demonstrate the new radar guns, the manufacturer has allowed the Youbet police department to use the guns for a short period of time. A random sample of 20 days in action shows that the new guns can detect a speeding vehicle at 2230 feet (mean) with a standard deviation of 72 feet. If the old guns and the new guns are equally accurate, should the department purchase the new radar guns?

Please fill out the following table based on your own calculation

                                                                                                

Old radar guns

2,217

old radar guns detect a speeding vehicle at a distance of 2217 feet

A random sample of 20 days

20

sample size

New radar guns

2,230

new radar guns detect a speeding vehicle at a distance of 2,230 feet

Sample std. dev.

72

a standard deviation of 72 feet

Step1 (a): write Down Your Hypothesis (H1):

Step 1(b): Write Down Your Null Hypothesis (H0)

Step 2: Standard Error (s.e.)

Step 3: Your Calculated T-score

Step 4: Degree Freedom

Step 5: The Corresponding P-value of Your Calculated T-score (P>?)

Step 6: Do You Reject or Accept Your Null Hypothesis and Why?

(Guide: If you get a p-value is greater than 0.05 (p>0.05), you can not reject the null hypothesis, but instead you need to Accept your null hypothesis)

Old radar guns

2,217

old radar guns detect a speeding vehicle at a distance of 2217 feet

A random sample of 20 days

20

sample size

New radar guns

2,230

new radar guns detect a speeding vehicle at a distance of 2,230 feet

Sample std. dev.

72

a standard deviation of 72 feet

Step1 (a): write Down Your Hypothesis (H1):

Step 1(b): Write Down Your Null Hypothesis (H0)

Step 2: Standard Error (s.e.)

Step 3: Your Calculated T-score

Step 4: Degree Freedom

Step 5: The Corresponding P-value of Your Calculated T-score (P>?)

Step 6: Do You Reject or Accept Your Null Hypothesis and Why?

(Guide: If you get a p-value is greater than 0.05 (p>0.05), you can not reject the null hypothesis, but instead you need to Accept your null hypothesis)

Explanation / Answer

Given that,
population mean(u)=2217
sample mean, x =2230
standard deviation, s =72
number (n)=20
null, Ho: =2217
alternate, H1: !=2217
level of significance, = 0.05
from standard normal table, two tailed t /2 =2.093
since our test is two-tailed
reject Ho, if to < -2.093 OR if to > 2.093
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =2230-2217/(72/sqrt(20))
to =0.8075
| to | =0.8075
critical value
the value of |t | with n-1 = 19 d.f is 2.093
we got |to| =0.8075 & | t | =2.093
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :two tailed ( double the one tail ) - Ha : ( p != 0.8075 ) = 0.4294
hence value of p0.05 < 0.4294,here we do not reject Ho
ANSWERS
---------------
null, Ho: =2217
alternate, H1: !=2217
test statistic: 0.8075
critical value: -2.093 , 2.093
decision: do not reject Ho
p-value: 0.4294
old guns and the new guns are equally accurate

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