Question

A nutritionist in the FDA wants to compare the caloric content of medium French fries sold by Wendonald (Population 1) and McKing (Population 2) fast-food chains, to see if there is any difference between them. To test this, random samples from each chain is taken and the caloric contents of French fries are measured. The finding is summarized in the table on next page. Conduct an independent-samples t test to test whether there is any difference between the caloric content of French fries sold by the two chains, following the steps below.

Wendonald	McKing
= 40	= 50
= 380 calories	= 360 calories
= 30 calories	= 38 calories

A. Write down the null and alternative hypotheses using proper notation

B. Calculate (Write all steps)

C. What is the value of for α = 0.05 with a two-tailed test?

D. Suppose your calculated t statistic is 2.90 (Note this is a hypothetical situation, not the actual result from your test), what decision do you make with respect to the statistical hypotheses for this study? State your interpretation with reference to the question asked.

Decision:

Interpretation:

Answer 1

Given that,
mean(x)=150
standard deviation , s.d1=199.2486
number(n1)=3
y(mean)=149.3333
standard deviation, s.d2 =182.5413
number(n2)=3
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =4.303
since our test is two-tailed
reject Ho, if to < -4.303 OR if to > 4.303
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =150-149.3333/sqrt((39700.0046/3)+(33321.32621/3))
to =0.0043
| to | =0.0043
critical value
the value of |t α| with min (n1-1, n2-1) i.e 2 d.f is 4.303
we got |to| = 0.00427 & | t α | = 4.303
make decision
hence value of |to | < | t α | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 0.0043 ) = 0.997
hence value of p0.05 < 0.997,here we do not reject Ho
ANSWERS
---------------
A.
null, Ho: u1 = u2
alternate, H1: u1 != u2
B.
T test for difference of means
C.
two tailed test
D.
test statistic: 0.0043
critical value: -4.303 , 4.303
decision: do not reject Ho
p-value: 0.997
we do not have enough evidence to support the claim that whether there is any difference between the caloric content of French fries sold by the two chains.