A professor at a local university conducted a survey of 125 businesses in a city
ID: 3310151 • Letter: A
Question
A professor at a local university conducted a survey of 125 businesses in a city to determine what motivates small businesses to export their products. The CEOs were asked to respond to the statement "Management believes that the business can achieve economies of scale by exporting" on a scale of 1 (strongly disagree) to 5 (strongly agree). Summary statistics for the n=140 scale scores were reported as x = 3.82 and s = 1.4. In his study, the professor hypothesized that if the true mean scale score exceeds 3.5, then CEOs at all businesses in the city generally agree with the statement. Complete parts a through c below.
Calculate the value of the test statistic
(Round to two decimal places as needed.)
Use technology to calculate the p-value
Round to three decimal places as needed
State the result of this test
Explain why the results of the study, although "statistically significant," may not be practically significant
The scale scores for the sample of 125 businesses are unlikely to be normally distributed. Does this invalidate the inference you made in part a? Explain
Explanation / Answer
Given that,
population mean(u)=3.5
sample mean, x =3.82
standard deviation, s =1.4
number (n)=140
null, Ho: =3.5
alternate, H1: >3.5
level of significance, = 0.1
from standard normal table,right tailed t /2 =1.288
since our test is right-tailed
reject Ho, if to > 1.288
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =3.82-3.5/(1.4/sqrt(140))
to =2.7045
| to | =2.7045
critical value
the value of |t | with n-1 = 139 d.f is 1.288
we got |to| =2.7045 & | t | =1.288
make decision
hence value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 2.7045 ) = 0.00385
hence value of p0.1 > 0.00385,here we reject Ho
ANSWERS
---------------
null, Ho: =3.5
alternate, H1: >3.5
test statistic: 2.7045
critical value: 1.288
decision: reject Ho
p-value: 0.00385
results of the study, although statistically significant
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