Homework SoursePrice cents per gallon Price per Gallon in dollars 2325 2325
Price (cents per gallon)
Price per Gallon (in dollars)
232.5
2.325
227.7
2.277
237.4
2.374
235.9
2.359
234.1
2.341
239.1
2.391
241.0
2.41
238.4
2.384
232.9
2.329
237.3
2.373
228.8
2.288
231.5
2.315
236.5
2.365
235.6
2.356
227.1
2.271
244.8
2.448
233.8
2.338
239.9
2.399
232.5
2.325
239.6
2.396
244.4
2.444
238.7
2.387
236.6
2.366
230.5
2.305
242.2
2.422
226.4
2.264
230.8
2.308
229.5
2.295
238.7
2.387
228.2
2.282
233.2
2.332
227.9
2.279
233.6
2.336
237.5
2.375
238.1
2.381
237.4
2.374
231.2
2.312
234.6
2.346
233.6
2.336
237.6
2.376
232.7
2.327
240.0
2.4
231.5
2.315
234.2
2.342
238.2
2.382
231.4
2.314
240.6
2.406
234.3
2.343
234.2
2.342
233.8
2.338
In this demo, we\'ll practice using Excel to compute p
-
values using
the t distribution.
The U.S. Energy Administration reported that the mean price for a gallon of regular gasoline in the United States was $2.36 (
in
2006). We want to determine if gasoline prices in the Lower Atlantic states are
lower
than the national average. This file
contains regular gasoline prices for a sample of 50 service stations from Lower Atlantic states. Use
= 0.01
as your level of
significance. (In this problem we do not know
.) We\'ll
be using the second column of numbers (the price in dollars).
1. Set up your hypotheses.
H
0
:
2.36
H
a
:
< 2.36
This is a hypothesis test
for an average, not a proportion. We also do not know
, so we\'ll have to use the sample standard
deviation
s
.
2.
Use Excel to compute the sample mean (xbar). Use =AVERAGE(B2:B51)
xbar = 2.3496
3. Use Excel to compute the standard deviation (s). Use =STDEV.S(B2:B51)
s = 0.04437
4. Compute your test statistic using parts 2 and 3.
=
0
/
=
2
.
3496
2
.
36
0
.
04437
/
50
=
1
.
657
5. Compute the degrees of freedom (n
-
1
).
n = 50, df = 50
-
1 = 49
6. To get the p
-
value for a
lower tail test
, type
=1
-
T.DIST.RT( your test statistic, your degrees of freedom)
in an empty cell.
To get the p
-
value for an
upper tail test
, type
=T.DIST.RT(your test statistic, your degrees of freedom)
in an empty cell.
To get the p
-
value for a
two
-
tailed test
:
-
If your
test statistic is negative
, type
=2*(1
-
T.DIST.RT( your test statistic, degrees of freedom))
-
If your
test statistic is positive
, type
=2*T.DIST.RT( your test statistic, degrees of freedom)
7. What is the p
-
value for this test?
We
have a lower tail test, so in Excel we type:
=1
-
T.DIST.RT(
-
1.657, 49)
The p
-
value is 0.0520.
8. If your p
-
value is less than
= 0.01 reject H0. If your p
-
value is greater than
=0.01 do not reject
H0
.
Our p
-
value is bigger
than 0.01, so we do not reject H0. We do not have enough evidence to say that the
average price of a gallon of gasoline is lower in the Lower Atlantic State
Solution
