Answer:
There is no effect of the good intentions i.e. to restrain their diet out of concern about their weight, have on their eating habits.
Step-by-step explanation:
The question is incomplete as some information is not provided, please refer below the remaining information of the question.
Here are the data on grams of potato chips consumed (note that the study report gave the standard error of the mean rather than the standard deviation):
Group n bar{x} s
Unrestrained 9 63.83 24.72
Restrained 11 34 39.8
a. The standard error of the difference between sample means (
±
0.0001
) is:
b. The critical value (
±
0.001
) from the t distribution for confidence interval 80 % using the conservative degrees of freedom is:
c. Give a 80 % confidence interval (
±
0.01
) that describes the effect of restraint:
Answer:
a) The standard error of the difference between sample means:
S
E = √
s
2
1 / n
1 + s
2
2
/n
2
= √
s
e
2
1
+ s
e
2
2
= √
24.72
2
+ 39.8
2
= 46.85
b) The degrees of freedom:
D
f = n
1 +
n
2 −
2
= 9 + 11 − 2
= 18
The confidence level = 0.80
The significance level, α = 0.20
The critical value from the t distribution for confidence interval 80%:
t
c
r
i
t
i
c
a
l = t
α
/
2
, d
f = t
0.10
,
18 = ± 1.33
c) The 80% confidence interval:
(
μ
1
−
μ
2
)
=
(
¯
x
1
−
¯
x
2
) ± t
⋅
S
E
=
(
63.83
−
34
)
± 1.33
×
46.85
=
29.83
±
62.31
−
32.48
<
(
μ
1
−
μ
2
)
< 92.14
As the interval contains the zero. So, it can be concluded that there is no effect of the good intentions i.e. to restrain their diet out of concern about their weight, have on their eating habits.
