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 measurelme 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 Date 1/25 3/19 5/30 7/3 9/13 11/7 Initial Depth, X 53.5 59.3 63.2 50.3 60.6 68.5 Depth Five Years Later, Y 52.1 59.5 59.7 51.7 55.9 71.7 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. OB Using the same dates maximizes the difference in water clarity. GrC. Using the same dates makes the second sample dependent on the first and reduces variability in water clarity attributable to date. O D. Those are the same dates that all biologists use to take water clarity samples. 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 %3! H Hd (Type integers or decimals. Do not round.) Determine the test statistic for this hypothesis test. 0.66 (Round to two decimal places as needed.) Find the P-value for this hypothesis test. P-value = (Round to three 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 measurelme 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 Date 1/25 3/19 5/30 7/3 9/13 11/7 Initial Depth, X 53.5 59.3 63.2 50.3 60.6 68.5 Depth Five Years Later, Y 52.1 59.5 59.7 51.7 55.9 71.7 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. OB Using the same dates maximizes the difference in water clarity. GrC. Using the same dates makes the second sample dependent on the first and reduces variability in water clarity attributable to date. O D. Those are the same dates that all biologists use to take water clarity samples. 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 %3! H Hd (Type integers or decimals. Do not round.) Determine the test statistic for this hypothesis test. 0.66 (Round to two decimal places as needed.) Find the P-value for this hypothesis test. P-value = (Round to three decimal places as needed.)
Algebra & Trigonometry with Analytic Geometry
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Chapter3: Functions And Graphs
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Solve the last question please
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
3
5
6
Date
1/25 3/19 5/30
7/3
9/13 11/7
Initial Depth, X;
53.5
59.3 63.2
50.3
60.6
68.5
Depth Five Years Later, Y
52.1
59.5 59.7
51.7
55.9 71,7
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.
OB Using the same dates maximizes the difference in water clarity.
GC. Using the same dates makes the second sample dependent on the first and reduces variability in water clarity attributable to date.
O D. Those are the same dates that all biologists use to take water clarity samples.
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
%3D
H Hd
(Type integers or decimals. Do not round.)
<'0
Determine the test statistic for this hypothesis test.
0.66 (Round to two decimal places as needed.)
Find the P-value for this hypothesis test.
P-value = (Round to three decimal places as needed.)
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