A researcher studies water clarity at the same location in a lake on the same da
ID: 3368264 • Letter: A
Question
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) and ?(b) below. Observation 1 2 3 4 5 6 Date ?1/25 ?3/19 ?5/30 ?7/3 ?9/13 ?11/7 Initial 49.7 67.1 57.4 49.3 50.7 72.4 After five years 46.5 74.7 61.5 50.9 58.6 77.3 ?(a) Why is it important to take the measurements on the same? date? A. Those are the same dates that all biologists use to take water clarity samples. B. Using the same dates makes the second sample dependent on the first. C. Using the same dates maximizes the difference in water clarity. D. Using the same dates makes it easier to remember to take samples. ?(b) Does the evidence suggest that the clarity of the lake is improving at the alpha equals 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. Choose the correct conclusion below. Reject Upper H 0. Do not reject Upper H 0.
Explanation / Answer
The statistical software output for this problem is:
Paired T hypothesis test:
?D = ?1 - ?2 : Mean of the difference between Initial and After 5 years
H0 : ?D = 0
HA : ?D ? 0
Hypothesis test results:
Hence,
a) Using the same dates makes the second sample dependent on the first. Option B is correct.
b) Do not reject Ho
Difference Mean Std. Err. DF T-Stat P-value Initial - After 5 years -3.8166667 1.6969417 5 -2.2491443 0.0744Related Questions
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