Question

Researchers at a food company are interested in how a new spaghetti sauce made from green tomatoes (and green in color) will compare to its traditional red spaghetti sauce. The company is worried that the green color will adversely affect the tastiness scores. It randomly assigns subjects to either the green or red sauce condition. Subjects indicate the tastiness of the sauce on a 10-point scale. Tastiness scores tend to be skewed. The scores follow:

RS GS

7 | 4

6 | 5

9 | 6

10 | 8

6 | 7

7 | 6

8 | 9

a. What statistical test should be used to analyze these data?

b. Identify H0 and Ha for this study.

c. Conduct the appropriate analysis.

d. Should H0 be rejected? What should the researcher conclude?

Answer 1

Given that,
mean(x)=7.5714
standard deviation , s.d1=1.5119
number(n1)=7
y(mean)=6.4286
standard deviation, s.d2 =1.7182
number(n2)=7
null, Ho: u1 = u2
alternate, H1: u1 != u2
level of significance, α = 0.05
from standard normal table, two tailed t α/2 =2.447
since our test is two-tailed
reject Ho, if to < -2.447 OR if to > 2.447
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =7.5714-6.4286/sqrt((2.28584/7)+(2.95221/7))
to =1.32
| to | =1.32
critical value
the value of |t α| with min (n1-1, n2-1) i.e 6 d.f is 2.447
we got |to| = 1.3211 & | t α | = 2.447
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 != 1.3211 ) = 0.235
hence value of p0.05 < 0.235,here we do not reject Ho
ANSWERS
---------------
a.
t test for difference of means
b.
null, Ho: u1 = u2
alternate, H1: u1 != u2
c.
test statistic: 1.32
critical value: -2.447 , 2.447
d.
decision: do not reject Ho
p-value: 0.235
we do not have enough evidence to support the claim that new spaghetti sauce made from green tomatoes (and green in color) will compare to its traditional red spaghetti sauce