1 NitrateLevel 2 50.1 3 48 4 46 5 45.9 6. 39.9 7 52.1

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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1 Nitratelevel
2
50.1
3
48
4
46
45.9
6.
39.9
7
52.1
8
43.4
45.6
10
47.2
11
48.1
12
43.8
13
49.1
14
44.4
15
51.8
16
41.7
Transcribed Image Text:1 Nitratelevel 2 50.1 3 48 4 46 45.9 6. 39.9 7 52.1 8 43.4 45.6 10 47.2 11 48.1 12 43.8 13 49.1 14 44.4 15 51.8 16 41.7
6.
A Waikato couple have decided to improve stock management practices
on their dairy farm as they are concerned about the amount of pollution that the
farm has caused in nearby waterways. They are particularly concerned about the
amount of nitrate run-off coming from their dairy herd. Until recently, nitrate levels
in their local river were often well above the MAV (maximum acceptable value) for
drinking water of 50mg/litre.
Once the final improvements on the farm were made, the farmers took frequent
measurements of nitrate levels in the river over a period of 6 months. They then
took a random sample of 15 of those measurements. These data are available
(a)
d.p.) and confidence interval (to 2 d.p.) for the
i. 95% confidence interval
ii. 99% confidence interval
Using Excel and the data provided, give the margin of error (to 3
of the nitrate levels in the river in mg/litre (to get the required accuracy you
will need to give your value of s to at least 3 dp). Explain briefly what the
95% CI tells us.
(b)
they have made have caused nitrate levels in the river to drop below the MAV.
Imagine that they have asked you to make use of your statistical knowledge.
Using iNZight and the data provided, conduct a one sample t-test (t-test of a
mean) using a significance level of a = 0.01. Clearly show all steps in your test,
including both hypotheses, the relevant information obtained from iNZight and
The farmers wish to test their hypothesis that the improvements
of course the conclusion.
What would have been the changes to your answer to question
(c)
6b if the farmers had wanted to test whether nitrate levels were significantly
different from the MAV?
(d)
Comment briefly on the suitability of the test carried out in question
Transcribed Image Text:6. A Waikato couple have decided to improve stock management practices on their dairy farm as they are concerned about the amount of pollution that the farm has caused in nearby waterways. They are particularly concerned about the amount of nitrate run-off coming from their dairy herd. Until recently, nitrate levels in their local river were often well above the MAV (maximum acceptable value) for drinking water of 50mg/litre. Once the final improvements on the farm were made, the farmers took frequent measurements of nitrate levels in the river over a period of 6 months. They then took a random sample of 15 of those measurements. These data are available (a) d.p.) and confidence interval (to 2 d.p.) for the i. 95% confidence interval ii. 99% confidence interval Using Excel and the data provided, give the margin of error (to 3 of the nitrate levels in the river in mg/litre (to get the required accuracy you will need to give your value of s to at least 3 dp). Explain briefly what the 95% CI tells us. (b) they have made have caused nitrate levels in the river to drop below the MAV. Imagine that they have asked you to make use of your statistical knowledge. Using iNZight and the data provided, conduct a one sample t-test (t-test of a mean) using a significance level of a = 0.01. Clearly show all steps in your test, including both hypotheses, the relevant information obtained from iNZight and The farmers wish to test their hypothesis that the improvements of course the conclusion. What would have been the changes to your answer to question (c) 6b if the farmers had wanted to test whether nitrate levels were significantly different from the MAV? (d) Comment briefly on the suitability of the test carried out in question
Expert Solution
Step 1

Answer:

 

(a) (i)

44.52 confidence interval 95.% lower
48.42 confidence interval 95.% upper
1.951 margin of error

(ii)

43.77 confidence interval 99.% lower
49.18 confidence interval 99.% upper
2.708 margin of error

The 95% confidence interval for the mean amount is between 44.52 and 48.42.

(b) The hypothesis being tested is:

H0: µ = 50

Ha: µ < 50

50.0000 hypothesized value
46.4733 mean NitrateLevel
3.5233 std. dev.
0.9097 std. error
15 n
14 df
   
-3.877 t
.0008 p-value (one-tailed, lower)

The p-value is 0.0008.

Since the p-value (0.0008) is less than the significance level (0.01), we can reject the null hypothesis.

Therefore, we can conclude that µ < 50.

(c) The hypothesis being tested is:

H0: µ = 50

Ha: µ ≠ 50

50.0000 hypothesized value
46.4733 mean NitrateLevel
3.5233 std. dev.
0.9097 std. error
15 n
14 df
   
-3.877 t
.0017 p-value (two-tailed)

The p-value is 0.0017.

Since the p-value (0.0017) is less than the significance level (0.01), we can reject the null hypothesis.

Therefore, we can conclude that µ < 50.

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