A health journal conducted a study to see if packaging a healthy food product li

Question

A health journal conducted a study to see if packaging a healthy food product like junk food would influence children's desire to consume the product. A fictitious brand of a healthy food

productlong dash—sliced

appleslong dash—was

packaged to appeal to children. The researchers showed the packaging to a sample of

363363

school children and asked each whether he or she was willing to eat the product. Willingness to eat was measured on a 5-point scale, with

1equals="not

willing at all" and

5equals="very

willing." The data are summarized as

x overbarxequals=3.293.29

and

sequals=2.042.04.

Suppose the researchers knew that the mean willingness to eat an actual brand of sliced apples (which is not packaged for children) is

muequals=33.

Complete parts a and b below.

a. Conduct a test to determine whether the true mean willingness to eat the brand of sliced apples packaged for children exceeded 3. Use

alphaequals=0.010.01

to make your conclusion.

State the null and alternative hypotheses.

Upper H 0H0:

mu not equals 33

mu greater than 3>3

mu equals 3=3

mu less than 3<3

Upper H Subscript aHa:

mu greater than 3>3

mu equals 3=3

mu not equals 33

mu less than 3<3

Find the test statistic.

zequals=nothing

(Round to two decimal places as needed.)

Find the p-value.

p-valueequals=nothing

(Round to three decimal places as needed.) What is the appropriate conclusion at

alphaequals=0.010.01?

A.

Do not rejectDo not reject

H0.

There is

sufficientsufficient

evidence to conclude that the true mean response for all school children is greater than

33.

B.

RejectReject

H0.

There is

sufficientsufficient

evidence to conclude that the true mean response for all school children is greater than

33.

C.

Do not rejectDo not reject

H0.

There is

insufficientinsufficient

evidence to conclude that the true mean response for all school children is greater than

33.

D.

RejectReject

H0.

There is

insufficientinsufficient

evidence to conclude that the true mean response for all school children is greater than

33.

b. The data (willingness to eat values) are not normally distributed. How does this impact (if at all) the validity of your conclusion in part

a?

Explain.

Explanation / Answer

n = 363

Xbar = 3.29

s = 2.04

a) Ho

mu equals 3=3

b)

Ha

mu greater than 3>3

c)

TS = (xbar - mu)/(s/sqrt(n))

= (3.29 - 3)/(2.04/sqrt(363))

= 2.708451

d)

p-value = P(t > 2.708451

= 0.0034

since p-value< 0.01

we reject the null hypothesis

there is sufficient evidence to conclude that the true mean response for all school children is greater than 3

option B) is correct

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