Construct a 90 confidence interval for the above data be

Question

Question 1- Some soap manufacturers sell special "antibacterial" soaps. However, one might expect ordinary soap to also kill bacteria. To investigate this, a researcher prepared a solution from ordinary, non-antibiotic soap and a control solution of sterile water. The two solutions were placed onto petridishes and E. coli bacteria were added. The dishes were incubated for 24 hours and the numbers of bacteria colonies on each dish were counted. The data are given in the following table.

	Control Group X	Soap Group Y
	30	76
	36	27
	66	16
	21	30
	63	26
	38	46
	35	6
	45
n	8	7
sample mean	41.8	32.4
sample sd	15.6	22.8

(a) Construct a 90% confidence interval for the above data Be sure to interpret this confidence interval in the context of this setting.

A test should be performed to determine whether soap more effective than the control. Conduct the hypothesis test at the 5% level.

(b) State the null and alternative hypotheses in words and symbols.

(c) Compute the test statistic

(d) Compute the P-value

(e) State the conclusion of the test in the context of this setting.

Question 2- Surfactants are chemical agents, such as detergents, that lower the surface tension of a liquid. Surfactants play an important role in the cleaning of contaminated soils. In an experiment to determine the effectiveness of a certain method for removing toluene from sand, the sand was washed with a surfactant, and then rinsed with de-ionized water. Of interest was the amount of toluene that came out in the rinse.
In five such experiments, the amounts of toluene removed in the rinse cycle, expressed as a percentage of the total amount originally present, were 5, 4.8, 9, 10, and 7.3.

(a) Find a 95% confidence interval for the percentage of toluene removed in the rinse.

(b) Conduct a hypothesis at the (Alpha)a = 5% level. Can you conclude that the mean amount of toluene removed in the rinse is less than 8%?

Question 3- Two formulations of a certain coating, designed to inhibit corrosion, are being tested. For each of eight pipes, half the pipe is coated with formulation A and the other half is coated with formulation B. Each pipe is exposed to a salt environment for 500 hours. Afterward, the corrosion loss (in μm) is measured for each formulation on each pipe.

Pipe	A	B
1	197	204
2	161	182
3	144	140
4	162	178
5	185	183
6	154	163
7	136	156
8	130	143

Can you conclude that the mean amount of corrosion differs between the two formulations?
Conduct a hypothesis test at the (Alpha)a = 10% significance level.
(a) State the appropriate null and alternative hypotheses.

(b) Compute the test statistic.

(c) Compute the P-value

(d) State the conclusion of the test in the context of this setting.

Question 4- A 95% confidence interval for μX - μY is (-0.3, 0.15). Based upon the data from which the confidence interval was constructed, someone wants to test H0:μX = μY versus Ha:μX 6= μY, at the (alpha) a = 5% significance level.

(a) Based upon the confidence interval, what is your conclusion of the hypothesis test? (Explain)

(b) Can we use the above confidence interval to conduct the hypothesis test at the (alpha) a = 10% level? Why or why not?

Question 5- Myocardial blood flow (MBF) was measured for two groups of subjects after five minutes of bicycle exercise. The normoxia ("normal oxygen") group was provided normal air to breathe whearas the hypoxia group was provided with a gax mixture with reduced oxygen to simulate high altitude. The results (ml/min/g) are shown in the table below.

	NORMOXIA X	HYPOXIA Y
	3.45	6.37
	3.09	5.69
	3.09	5.58
	2.65	5.27
	2.49	5.11
	2.33	4.88
	2.28	4.68
	2.24	3.5
	2.17
	1.34
n	10	8
sample mean	2.51	5.14
sample sd	0.6	0.84

We wish to investigate the effect of hypoxia on MBF.

(a) Construct a 90% confidence interval for the differences of the mean MBF for the two groups, i.e. μx μy.

(b) Use the above confidence interval to conduct a hypothesis test with α = 0.10.