The Laughing Stock Unit of the New York Comedy Department (NYCD) is considering
ID: 2929593 • Letter: T
Question
The Laughing Stock Unit of the New York Comedy Department (NYCD) is considering the purchase of new belly-laugh meters. On average, the laugh-o-meter presently used by the department can detect a guffaw at a distance listed below. In order to demonstrate the new meters, the manufacturer has allowed the NYCD to use the detectors for a short period of time. A random sample shows the distance at which the new meters can detect a bad joke in feet (mean) with a sample standard deviation.
Current laugh-o-meter detection range in feet: 75
New meter detection range in feet (mean from sample): 100
Standard deviation from sample: 72
Sample size (n): 36
a) State the null and alternative hypothesis.
b) Should the department purchase the new laugh-o-meters?
(You need to calculate a 95% confidence interval, or a t score, but also use your gut to check the answer. Remember the rule that less than 2 standard errors from the mean, the result is not unusual.) Show your work.
Explanation / Answer
Given that,
population mean(u)=75
sample mean, x =100
standard deviation, s =72
number (n)=36
null, Ho: =75
alternate, H1: >75
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.69
since our test is right-tailed
reject Ho, if to > 1.69
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =100-75/(72/sqrt(36))
to =2.083
| to | =2.083
critical value
the value of |t | with n-1 = 35 d.f is 1.69
we got |to| =2.083 & | t | =1.69
make decision
hence value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 2.0833 ) = 0.0223
hence value of p0.05 > 0.0223,here we reject Ho
ANSWERS
---------------
null, Ho: =75
alternate, H1: >75
test statistic: 2.083
critical value: 1.69
decision: reject Ho
p-value: 0.0223
we have evidence to support the claim
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