A researcher studies water clarity at the same location in a lake on the same dates during the course of a year and repeats the measurements on the same dates 5 years later. The researcher immerses a weighted disk painted black and white and measures the depth (in inches) at which it is no longer visible. The collected data is given in the table below. Complete parts (a) through (c) below. Observation 3 4 5 Date 1/25 3/19 5/30 7/3 9/13 11/7 Initial Depth, X, Depth Five Years Later, Y 72.1 70.2 46,4 50.2 42.3 55.1 79.0 70.1 51.6 54.0 48.6 57.6 a) Why is it important to take the measurements on the same date? O A. Using the same dates makes it easier to remember to take samples. O B. Those are the same dates that all biologists use to take water clarity samples. c. Using the same dates makes the second sample dependent on the first and reduces variability in water clarity attributable to date. O D. Using the same dates maximizes the difference in water clarity. b) Does the evidence suggest that the clarity of the lake is improving at the a = 0.05 level of significance? Note that the normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. Let d, = X, - Y,. Identify the null and alternative hypotheses. Ho: Ha H,: Hd < 0 (Type integers or decimals. Do not round.) Determine the test statistic for this hypothesis test. (Round to two decimal places as needed.)
A researcher studies water clarity at the same location in a lake on the same dates during the course of a year and repeats the measurements on the same dates 5 years later. The researcher immerses a weighted disk painted black and white and measures the depth (in inches) at which it is no longer visible. The collected data is given in the table below. Complete parts (a) through (c) below. Observation 3 4 5 Date 1/25 3/19 5/30 7/3 9/13 11/7 Initial Depth, X, Depth Five Years Later, Y 72.1 70.2 46,4 50.2 42.3 55.1 79.0 70.1 51.6 54.0 48.6 57.6 a) Why is it important to take the measurements on the same date? O A. Using the same dates makes it easier to remember to take samples. O B. Those are the same dates that all biologists use to take water clarity samples. c. Using the same dates makes the second sample dependent on the first and reduces variability in water clarity attributable to date. O D. Using the same dates maximizes the difference in water clarity. b) Does the evidence suggest that the clarity of the lake is improving at the a = 0.05 level of significance? Note that the normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. Let d, = X, - Y,. Identify the null and alternative hypotheses. Ho: Ha H,: Hd < 0 (Type integers or decimals. Do not round.) Determine the test statistic for this hypothesis test. (Round to two decimal places as needed.)
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter87: An Introduction To G- And M-codes For Cnc Programming
Section: Chapter Questions
Problem 22A
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Question
Help finding:
- test statistic
- to=
- P value=
- Draw a boxplot of the differenced data. Does this visual evidence support the results obtained in part b)?
Transcribed Image Text:A researcher studies water clarity at the same location in a lake on the same dates during the course of a year and repeats the measurements on the same dates 5 years later. The researcher immerses a weighted disk painted
black and white and measures the depth (in inches) at which it is no longer visible. The collected data is given in the table below. Complete parts (a) through (c) below.
Observation
1
2
4
6
Date
1/25
3/19
5/30
7/3
9/13
11/7
Initial Depth, X;
72.1
70.2
46.4
50.2
42.3
55.1
Depth Five Years Later, Y;
79.0
70.1
51.6
54.0
48.6
57.6
.....
a) Why is it important to take the measurements on the same date?
A. Using the same dates makes it easier to remember to take samples.
B. Those are the same dates that all biologists use to take water clarity samples.
C. Using the same dates makes the second sample dependent on the first and reduces variability in water clarity attributable to date.
D. Using the same dates maximizes the difference in water clarity.
b) Does the evidence suggest that the clarity of the lake is improving at the a = 0.05 level of significance? Note that the normal probability plot and boxplot of the data indicate that the differences are approximately normally
distributed with no outliers.
Let d; = X; - Y;. Identify the null and alternative hypotheses.
Ho: Hd
H1: Hd
(Type integers or decimals. Do not round.)
Determine the test statistic for this hypothesis test.
(Round to two decimal places as needed.)
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