Phosphorous is a chemical that is found in many household cleaning products. Unfortunately, phosphorous also finds its way into surface water, where it can harm fish, plants, and other wildlife. Two methods of phosphorous reduction are being studied. At a random sample of 7 locations, both methods were used and the total phosphorous reduction (mg/L) was recorded. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer. Things that are labelled i underneath a b c, etc are all part of that part.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Topic Video
Question

Phosphorous is a chemical that is found in many household cleaning products. Unfortunately, phosphorous also finds its way into surface water, where it can harm fish, plants, and other wildlife. Two methods of phosphorous reduction are being studied. At a random sample of 7 locations, both methods were used and the total phosphorous reduction (mg/L) was recorded. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer.

Things that are labelled i underneath a b c, etc are all part of that part.

 
 
Phosphorous is a chemical that is found in many household cleaning products. Unfortunately, phosphorous also finds its way into surface water, where it can harm fish, plants,
and other wildlife. Two methods of phosphorous reduction are being studied. At a random sample of 7 locations, both methods were used and the total phosphorous reduction
(mg/L) was recorded. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the
P-value a small amount and thereby produce a slightly more "conservative" answer.
Site
Method I:
1
2
3
4
6
7
0.055
0.039
0.013
0.015
0.007
0.017
0.020
0.002
0.010
Method II:
0.014
0.045
0.017
0.001
0.013
Do these data indicate a difference (either way) in the average reduction of phosphorous between the two methods? Use a = 0.05. (Let d = Method I – Method II.)
State the null and alternate hypotheses.
O Ho: Hd> 0; H1: Hd = 0
O Ho: Hd = 0; H1: Hd# 0
O Ho: Hd = 0; H1: Hd> 0
O Ho: Hd = 0; H1: Hd < 0
(ii) What sampling distribution will you use? What assumptions are you making?
O The Student's t. We assume that d has an approximately uniform distribution.
O The standard normal. We assume that d has an approximately normal distribution.
O The standard normal. We assume that d has an approximately uniform distribution.
O The Student's t. We assume that d has an approximately normal distribution.
What is the value of the sample test statistic? (Round your answer to three decimal places.)
(iii) Find (or estimate) the P-value.
O P-value > 0.500
O 0.250 < P-value < 0.500
O 0.100 < P-value < 0.250
O 0.050 < P-value < 0.100
O 0.010 < P-value < 0.050
O P-value < 0.010
Sketch the sampling distribution and show the area corresponding to the P-value.
a
b
2.
4
-2
2
4.
C
d
2
4
-4
-2
2
4
(iv) Based on your answers in parts (i) to (iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a?
O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(iv) Based on your answers in parts (i) to (iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a?
O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(v) Interpret your conclusion in the context of the application.
O There is sufficient evidence at the 0.05 level to conclude that there is a difference in phosphorous reduction between the two methods.
O There is insufficient evidence at the 0.05 level to conclude that there is a difference in phosphorous reduction between the two methods.
Transcribed Image Text:Phosphorous is a chemical that is found in many household cleaning products. Unfortunately, phosphorous also finds its way into surface water, where it can harm fish, plants, and other wildlife. Two methods of phosphorous reduction are being studied. At a random sample of 7 locations, both methods were used and the total phosphorous reduction (mg/L) was recorded. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value a small amount and thereby produce a slightly more "conservative" answer. Site Method I: 1 2 3 4 6 7 0.055 0.039 0.013 0.015 0.007 0.017 0.020 0.002 0.010 Method II: 0.014 0.045 0.017 0.001 0.013 Do these data indicate a difference (either way) in the average reduction of phosphorous between the two methods? Use a = 0.05. (Let d = Method I – Method II.) State the null and alternate hypotheses. O Ho: Hd> 0; H1: Hd = 0 O Ho: Hd = 0; H1: Hd# 0 O Ho: Hd = 0; H1: Hd> 0 O Ho: Hd = 0; H1: Hd < 0 (ii) What sampling distribution will you use? What assumptions are you making? O The Student's t. We assume that d has an approximately uniform distribution. O The standard normal. We assume that d has an approximately normal distribution. O The standard normal. We assume that d has an approximately uniform distribution. O The Student's t. We assume that d has an approximately normal distribution. What is the value of the sample test statistic? (Round your answer to three decimal places.) (iii) Find (or estimate) the P-value. O P-value > 0.500 O 0.250 < P-value < 0.500 O 0.100 < P-value < 0.250 O 0.050 < P-value < 0.100 O 0.010 < P-value < 0.050 O P-value < 0.010 Sketch the sampling distribution and show the area corresponding to the P-value. a b 2. 4 -2 2 4. C d 2 4 -4 -2 2 4 (iv) Based on your answers in parts (i) to (iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (iv) Based on your answers in parts (i) to (iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (v) Interpret your conclusion in the context of the application. O There is sufficient evidence at the 0.05 level to conclude that there is a difference in phosphorous reduction between the two methods. O There is insufficient evidence at the 0.05 level to conclude that there is a difference in phosphorous reduction between the two methods.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps

Blurred answer
Knowledge Booster
Hypothesis Tests and Confidence Intervals for Means
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman