Statistics Hypothesis: Dissolved Oxygen Concentration

Please show all the step as required.

Note: For hypothesis testing, the following procedure is recommended:

- Step 1: State H0 an H1, Choose
- Step 2: Determine Population Parameters [if possible] and Sample Statistics
- Step 3: Determine Statistical Technique for Use
- Step 4: Determine Rejection Region Based on Critical Values [corresponding to the level of significance given]
- Step 5: Calculate Test Statistics
- Step 6: Compare Test Statistics to Critical Value
- Step 7: Statistical Decision

Question 1

The daily dissolved oxygen concentration (DO) for a location A downstream of an industrial plant has been recorded for the past 10 consecutive days as tabulated below:

Day DO (mg/l)
1 1.8
2 2
3 2.1
4 1.7
5 1.2
6 2.3
7 2.5
8 2.9
9 1.9
10 2.2

a. Assuming that DO has a normal distribution N (µ, σ), what can be delivered in relation to µ based on the obtained data?

b. Suppose the minimum concentration of DO required by the Environmental Protection Agency [EPA] is 2.0 mg/l. Assume that the probability distribution of DO is unknown; perform a hypothesis test to determine whether the stream quality satisfies the EPA standard at the significance level of 5%.

c. Determine the 95% confidence interval for the true mean DO concentration.

Question 2

To assess the effect of an in-vehicle navigation device on travel-time savings, an experiment was conducted in which five people drove from the same origin and to the same destination with and without using the device. The results are shown below.

Driver Travel Time
Without Navigation Device With Navigation Device
1 30 28
2 32 26
3 30 25
4 28 27
5 28 26

Perform a hypothesis test to determine whether the use of the device has led to a statistically significant reduction in travel times at the 5% level of significance.