Assignment Directions:Please answer all questions in a word document.If a series of calculations is necessary in order to arrive at a final answer, show your work at major stages in the calculation process.This way I can give partial credit and identify where mistakes may have been made.If you are asked to explain something, provide as much detail as possible.

NOTE:For problems involving classical hypothesis testing, complete the five steps discussed in class and state the relevance of your findings in terms of the original statement of the problem. I have included a write up of the steps used in our classical hypothesis testing example after the problems.

1.Mean annual water consumption per household in a city is 6800 L, with a standard deviation of 1200 L.If a random sample of 40 households in a neighborhood reveals a mean water consumption of 7100 L, test the hypothesis that the sample households have a different consumption level than the average city household.Assume that = .10.

H0 = 6800 and HA = 6800

a = .10 = 90% confidence interval

Z = (X - ) /

Z = (7100 - 6800) / 1200 = 0.25

Z = 0.25

This values lies in the critical region of the two tailed test, so there is a difference.

2. A stream has been monitored unit for a number of years, and the total dissolved solids in the stream averages 40 parts per million.Following a recent change in land use in the drainage basin of the stream, a fluvial geomorphologist finds that the mean parts per million of dissolved solids in a 25-weeksampleis 52, with asample standard deviationof 32.Has there been a change in the average level of dissolved solids in this stream?Assume a normal population and that = .10.

We will adopt the 10% level, which means a = .10

Two Tailed Test HO= 40 and HA= 40.

T statistic: t = (52-40) /(32/5) = 1.88

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NOTE: For problems involving hypothesis testing, you need to complete the five steps discussed in class and state the relevance of your findings in terms of the original statement of the problem. Below is an illustration of how this would be done for the problem covered in lecture.

Step 1.

HO:= 3.2(The sample data were taken from a population with a mean of 3.2.)

HA:3.2(The sample data were not taken from a population with a mean of 3.2.)

Step 2.

Since the sample size is 30 (n = 100), is known, and we are working with one sample, we use a one-sample z-test.

Step 3. = .05

Step 4.

Since = .05, we have the following:

Thus we will reject Ho if z > 1.96 or if z < -1.96.

Step 5.

Reject Ho and conclude that the sample does not appear to be representative of the population; more specifically, there is a bias toward larger households in the sample.