A professor at a local university conducted a survey of 134134

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 equals 134n=134

scale scores were reported as x overbarxequals=3.843.84

and ssequals=1.61.6.

In his study, the professor hypothesized that if the true mean scale score exceeds 3.53.5,

then CEOs at all businesses in the city generally agree with the statement. Complete parts a through c below.

a. Conduct the appropriate test using aequals=0.050.05.

State your conclusion in the words of the problem.

State the null and alternative hypotheses.

A.

Upper H 0H0:

munot equals3.53.5

Upper H Subscript aHa:

muequals=3.53.5

B.

Upper H 0H0:

muequals=3.53.5

Upper H Subscript aHa:

muless than<3.53.5

C.

Upper H 0H0:

muequals=3.53.5

Upper H Subscript aHa:

mugreater than>3.53.5

D.

Upper H 0H0:

muequals=3.53.5

Upper H Subscript aHa:

munot equals3.53.5

Calculate the value of the test statistic.

zequals=nothing

(Round to two decimal places as needed.)

Use technology to calculate the p-value.

p-valueequals=nothing

(Round to three decimal places as needed.)

State the result of this test.

A.

Upper H 0H0

is not rejectednotrejected

at the alphaequals=0.050.05

level of significance. There is sufficientsufficient

evidence to conclude that the true mean scale score exceeds 3.53.5.

B.

Upper H 0H0

is not rejectednotrejected

at the alphaequals=0.050.05

level of significance. There is insufficientinsufficient

evidence to conclude that the true mean scale score exceeds 3.53.5.

C.

Upper H 0H0

is rejectedrejected

at the alphaequals=0.050.05

level of significance. There is sufficientsufficient

evidence to conclude that the true mean scale score exceeds 3.53.5.

D.

Upper H 0H0

is rejectedrejected

at the alphaequals=0.050.05

level of significance. There is insufficientinsufficient

evidence to conclude that the true mean scale score exceeds 3.53.5.

b. Explain why the results of the study, although "statistically significant," may not be practically significant.

A.

The results of the study may not be practically significant because the standard deviation is too large for the sample size.

B.

The results of the study may not be practically significant because the sample size is large.

C.

The results of the study may not be practically significant because the sample mean is close to the assumed true mean, and both values are between 3.5 and 4 for a test that only produces whole number results.

D.

The results of the study may not be practically significant because alphaequals=0.050.05.

c. The scale scores for the sample of 134134

businesses are unlikely to be normally distributed. Does this invalidate the inference you made in part a?

Explain.

A.

Yes, because the sample size is less than 300.

B.

Yes, because the sample size is greater than 30.

C.

No, because the sample size is greater than 30.

D.

No, because the sample size is less than 300.