In this problem, assume that the distribution of differences is approximately normal.Note: For degrees of freedomd.f. not in the Student'st table, use the closestd.f. that issmaller. In some situations, this choice ofd.f. may increase theP-value by a small amount and therefore produce a slightly more "conservative" answer.
Is fishing better from a boat or from the shore? Pyramid Lake is located on the Paiute Indian Reservation in Nevada. Presidents, movie stars, and people who just want to catch fish go to Pyramid Lake for really large cutthroat trout. Let rowB represent hours per fish caught fishing from the shore, and let rowA represent hours per fish caught using a boat. The following data are paired by month from October through April.
|
Oct |
Nov |
Dec |
Jan |
Feb |
March |
April |
B: Shore |
1.4 |
1.9 |
2.0 |
3.2 |
3.9 |
3.6 |
3.3 |
A: Boat |
1.3 |
1.5 |
1.5 |
2.2 |
3.3 |
3.0 |
3.8 |
Use a 1% level of significance to test if there is a difference in the population mean hours per fish caught using a boat compared with fishing from the shore. (Letd =B −A.)
(a) What is the level of significance?
=__
State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
A-H
0: ?
d
= 0;H
1: ?
d
> 0; right-tailed
B-H
0: ?
d
≠ 0;H
1: ?
d
= 0; two-tailed
C-H
0: ?
d
= 0;H
1: ?
d
≠ 0; two-tailed
D-H
0: ?
d
= 0;H
1: ?
d
< 0;="">
(b) What sampling distribution will you use? What assumptions are you making?
A-The standard normal. We assume thatd has an approximately uniform distribution.
B-The standard normal. We assume thatd has an approximately normal distribution.
C-The Student'st. We assume thatd has an approximately uniform distribution.
D-The Student'st. We assume thatd has an approximately normal distribution.
What is the value of the sample test statistic? (Round your answer to three decimal places.)
(c) Find (or estimate) the
P-value.
A-P-value > 0.500
B-0.250 P-value <>
C-0.100 P-value <>
D-0.050 P-value <>
E-0.010 P-value <>
F-P-value <>
Sketch the sampling distribution and show the area corresponding to the
P-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??
A-At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
B-At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.
C-At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.
D-At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) State your conclusion in the context of the application.
A-Reject the null hypothesis, there is sufficient evidence to claim a difference in population mean hours per fish between boat fishing and shore fishing.
B-Fail to reject the null hypothesis, there is insufficient evidence to claim a difference in population mean hours per fish between boat fishing and shore fishing
C-Fail to reject the null hypothesis, there is sufficient evidence to claim a difference in population mean hours per fish between boat fishing and shore fishing.
D-Reject the null hypothesis, there is insufficient evidence to claim a difference in population mean hours per fish between boat fishing and shore fishin