1)You get a job as a traveling salesperson for Callahan Brake pads. You try to sell your
first client on the idea that Callahan Brake pads are superior in quality. The client agrees
but claims that your product is too expensive. He provides the following figures to
support his claim. Callahan Brakes pads cost $15 per pair. The average cost of your 5
leading competitors $13.62 with s = 1.09. Conduct a one-sample hypothesis test (alpha =
.05) to determine if the cost of Callahan Brake pads are in fact different from average.
Ho:  = 15
tcrit = 2.776
Ha:   15
tobs
= (M - ) / [s / sqrt(n)]
= 13.62 - 15 / (1.09 / sqrt(5)
= -1.38 / (1.09 / 2.24)
= -1.38 / .49
= -2.82
Because tobs falls in the rejection region, we would reject the null: t(4) = -2.82, SEM =
.49, p < .05. Unfortunately, this means that Callahan brake pads are more expensive than
average.
2) Use SPSS to determine if Amherst students are eating enough fruit. Assume that the
USRDA is 3 pieces of fruit. Set alpha = .01.
One-Sample Statistics
N
Fruits
Mean
124
Std. Deviation
2.102
Std. Error Mean
2.1834
.1961
One-Sample Test
Test Value = 3
95% Confidence Interval of the
Difference
t
Fruits
-4.578
df
Sig. (2-tailed)
123
.000
Mean Difference
-.8976
Lower
-1.286
Upper
-.509
The data indicate that the average Amherst student eats 2.102 pieces of fruit per day. The
p-value (.000) was less than alpha (.05). The hypothesis test indicates that this is
significantly below the US RDA of 3 servings of fruit per day: t (123) = -4.578, SEM
0.20, p < .05. Apparently, y’all need to eat more fruit!
3) You and Biff are playing a heated game of Jacks, when the conversation invariably
turns to who is the superior player. You both know enough statistics to know that one
game won't settle the matter completely. So, you each play six games, you pick up 5, 4,
8, 4, 5, and 6 jacks. Biff picks up 4, 4, 5, 3, 4, and 5 jacks. Conduct a two-sample t-test
(alpha = .05) to determine who is the better jackster. Do the calculations by hand, but you
may check your work with SPSS.
You
5, 4, 8, 4, 5, 6
(x) = 32
 (x2) = 182
Mean = 5.33
s = 1.51
Ho: y = b
Ho: y  b
s2 p
s2 p
SE
tobs
Biff
4, 4, 5, 3, 4, 5
(x) = 25
 (x2) = 107
Mean = 4.17
s = .75
tcrit = 2.228
= n1-1 (s21) + n2-1 (s22) / n1 + n2 - 2
= (6-1)(1.512) + (6-1)(.752) / 6 + 6- 2
= [(5) (2.267) + (5) (.567)] / 10
= 11.33 + 2.83 / 10
= 14.167 / 10
or
= SS1 + SS2 / df1 + df2
= 11.33 + 2.83 / 5 + 5
= 14.167 / 10
= s2p / n1 + s2p / n1
= 1.42 / 6 + 1.42 / 6
= .472
= 1.42
= 1.42
= .687
= (Meany - Meanb) / (SE)
= 5.33 - 4.17 / .687
= 1.16 / .687
= 1.69
Because tobs does not fall in the rejection region, we would fail to reject the null: t(10) =
1.69, SEM = .687, p> .05. This means that you do not have enough evidence to conclude
that you are a better jackster than Biff.
4) Use SPSS to perform a two-sample t-test to determine if Amherst students consume
different amounts of fruits and vegetables (hint: is this a paired test or an independent
test). Set alpha = .01.
Paired Samples Statistics
Mean
Pair 1
N
Std. Deviation
Std. Error Mean
Fruits
2.102
124
2.1834
.1961
Veggies
2.212
124
1.2920
.1160
Paired Samples Test
Paired Differences
95% Confidence Interval
Mean
Pair 1
Std. Deviation Std. Error Mean
Lower
Upper
t
df
Sig. (2-tailed)
Fruits -.1097
2.3765
.2134
-.5321
.3128
-.514
123
Veggies
This is a paired t-test because each subject in the sample contributed two pieces of data
(one for fruit, one for vegetables). The mean servings of fruit and vegetables are 2.102
and 2.212, respectively; thus, the mean difference score was -0.1097. The paired t-test
revealed no significant difference in food consumption as the p-value (.608) was greater
than alpha (.05): t(123) = -0.514, SEM = 0.213, p > .01. Thus, there is not enough
evidence to conclude that Amherst students’ fruit and vegetable consumption differ from
one another.
5) Use SPSS to determine whether females and males consume the same amount of
vegetables? Set alpha to be an appropriate level.
Group Statistics
Gender
Veggies
N
Mean
Std. Deviation
Std. Error Mean
Female
87
2.218
1.2615
.1352
Male
37
2.197
1.3789
.2267
.608
Independent Samples Test
Levene's Test for
Equality of
Variances
t-test for Equality of Means
95% Confidence Interval
F
Veggies
Equal
variances
.693
Sig.
.407
t
.083
df
122
Sig. (2-
Mean
Std. Error
tailed)
Difference
Difference
.934
.0211
of the Difference
Lower
.2546
This should be an independent t-test because males and females represent two distinct
groups. The mean number of servings of vegetables per day for the males and females
were 2.197 and 2.218, respectively. The t-test revealed that the difference between the
males and females is not significant: t(122) = 0.083, SEM = 0.2546, p > .05. The results
of our test suggest that there is not enough evidence to conclude that there are gender
differences in vegetable consumption. Note: every other year that I have used this
example, females have eaten more veggies than males and ‘real’ data confirms this
gender difference).
-.4829
Upper
.5251