Geography 226: Lab 4

Geography 226

Lab 4

Statistical Estimation

Logic, like whiskey, loses its beneficial effect

when taken in too large quantities.

- Lord Dunsany -

1. In June 2000, water contaminated with fecal coliform bacteria, specifically Esherichia coli, led to the death of several people in Walkerton, Ontario. These bacteria have been associated with drinking water problems across the country and are also the reason for many beach and shellfish closures in BC’s coastal waters.

The general standards for fecal coliform are 50 MPN*/100ml in drinking water (MPN = most probable number of bacterium). The file Water.sav contains bacterial counts from a water quality sample in a drinking water reservoir. Using these data:

Determine the best estimate of average number of bacteria per 100 ml in the reservoir. (1)

b. Calculate the 90%, 95% and 99% confidence intervals for this sample. Summarize the steps and the results in a table. Compare the width of the three intervals. (12)

Steps	Interval A 90%	Interval B 95%	Interval C 99%
1. point estimate
2.Type of distribution
3. Confidence level
4. Tail
5. df and value
6. Formula and CI calc.
7.Interval

c. In a paragraph, briefly summarize the health risks associated with fecal coliform bacteria. You may use the internet as a research tool. Be sure to state your information sources. Which level of confidence would you use in your analyses? Explain your rationale. (5)

d. Calculate whether this sample will exceed the water quality standards for fecal coliform .This essentially means: would you drink this water? (use the confidence level you think is most appropriate.)
Show the 7 steps as you did above and give confidence statement. (5)

2. You are given another sample of bacterial counts where = 33 MPN/100ml, s = 5.3 MPN/100ml and n=30.

Is it clear which probability distribution you should use for the confidence intervals? Why or why not? (2)

b. Calculate the 99% confidence interval around the estimate using the Z and t distributions. Show all 7 steps . (8)

Interval A Z distribution	Interval B t distribution

c. Which interval is wider? Which confidence interval would you use for this sample? Why? (2)

3. Mangrove forests grow in the sheltered intertidal areas of tropical coastlines. Mangroves play a vital role in the coastal ecosystem, supporting many species of fish, invertebrates, insects, birds and animals. These forests also protect the coastline from the natural erosional processes (littoral drift, tidal currents and hurricanes).

In many countries, mangrove forests are cleared to make room for commercial ventures such as aquaculture, rice paddy agriculture and resort development. To help restore some natural habitat and protect the coastline, several countries (including India, Bangladesh, and Ecuador) have implemented mangrove-replanting programs.

In the first two years after planting, many seedlings are killed by masses of algae that wash up on shore. In a coastal mudflat in northwest India, a survey was conducted to assess seedling survival. Of 130 seedlings that were planted, 98 survived after two years.

What is the best estimate of the proportion of seedlings that survived? (1)

b. Calculate a 95% confidence interval for this estimate. Showing all 7 steps and give a confidence statement (5)

Steps
1.
2.
3.
4.
5.
6.
7.

c. If the survival rate is less than 70%, the area must be planted again. Use a one-tailed 95% confidence interval to determine if the area should be replanted. Based on your results, what action will you recommend? (7 steps and confidence statement to be included please.) (5)

Steps
1.
2.
3.
4.
5.
6.
7.

4. A smaller sample of 90 seedlings was taken to assess the seedling height growth of two mangrove species. The sample is summarized below:

Species name	Avicennia marina	Avicennia officinalis
Mean height	86 cm	71 cm
Median height	82 cm	73 cm
Standard deviation	23 cm	23 cm
Number of seedlings	35	55
Distribution shape	Normal	Normal

Which statistic will provide the best estimate of the true average seedling height for each species? (1)

b. Calculate a 90% confidence interval around the estimates. (8)

Steps	A. Marina	A. Officinalis
1.
2.
3.
4.
5.
6.
7.

c. Compare the width of the intervals. Is one interval wider? Why? What does this mean in terms of our confidence in the estimate? (4)

Mangrove information adapted from: Clark, J.R.1996. Coastal Zone Management Handbook. CRC Press: Florida.

Use the 6 Steps for Calculating Confidence Intervals from the lab manual. Show all lab work, including calculations, tables and/or diagrams. Ensure that your explanations are clear and well written.
Marking Guide (Lab Total = 59)

Question		Mark	Question		Mark
Q1	a	1	Q3	a	1
	b	12		b	5
	c	5		c	5
	d	5	Q4	a	1
Q2	a	2		b	8
	b+c	8+2		c	4