The level of dissolved oxygen in a river is an important indicator of the water’s ability to support aquatic life. A research project is started to determine if the oxygen levels in the river have changed. It is known from a study done 10 years prior, that the mean oxygen levels in milligrams per liter for the river was 4.3. a- Write appropriate hypotheses for this test b- You collect water samples at 15 randomly chosen locations along the river and measure the dissolved oxygen. Here are your results in milligrams per liter: 4.53 5.5 4.01 5.04 4.83 4.66 3.29 4.4 2.87 5.23 5.42 5.73 4.13 6.38 5.55 Construct and interpret a 95% confidence interval for the mean dissolved oxygen level for this stream. c- Using the sample from part b, conduct a significance test of these results using a 5% significance level. Give complete results of the test including a p-value and an interpretation of the test results that someone not in this class could understand
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The level of dissolved oxygen in a river is an important indicator of the water’s ability to support aquatic life. A research project is started to determine if the oxygen levels in the river have changed. It is known from a study done 10 years prior, that the mean oxygen levels in milligrams per liter for the river was 4.3.
a- Write appropriate hypotheses for this test
b- You collect water samples at 15 randomly chosen locations along the river and measure the dissolved oxygen. Here are your results in milligrams per liter:
| 4.53 | 5.5 | 4.01 |
| 5.04 | 4.83 | 4.66 |
| 3.29 | 4.4 | 2.87 |
| 5.23 | 5.42 | 5.73 |
| 4.13 | 6.38 | 5.55 |
Construct and interpret a 95% confidence interval for the mean dissolved oxygen level for this stream.
c- Using the sample from part b, conduct a significance test of these results using a 5% significance level. Give complete results of the test including a p-value and an interpretation of the test results that someone not in this class could understand
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