Question

1.

DDT is a pesticide banned in the United States for its danger to humans and animals. In an experiment on the impact of DDT, six rats were exposed to DDT poisoning and six rats were not exposed. For each rat in the experiment, a measurement of nerve sensitivity was recorded. The researchers suspected that the mean nerve sensitivity for rats exposed to DDT is greater than that for rats not poisoned. The data follow:

Poisoned rats:	12.207	16.869	25.050	22.429	8.456	20.589
Unpoisoned rats:	11.074	9.686	12.064	9.351	8.182	6.642

Let μ ₁ be the mean nerve sensitivity for rats poisoned with DDT. Let μ ₂ be the mean nerve sensitivity for rats not poisoned with DDT.

The (Option 1) less conservative computed degrees of freedom is:

	A.	7
	B.	4.
	C.	5.
	D.	6.

2,

An SRS of 100 flights of a large airline (airline 1) showed that 64 were on time. An SRS of 100 flights of another large airline (airline 2) showed that 80 were on time. Let p ₁ and p ₂ be the proportion of all flights that are on time for these two airlines. Using a 0.01 level of significance, what conclusion would you draw from this test?

	A.	accept the null hypothesis
	B.	fail to reject the null hypothesis; there is not strong enough evidence
	C.	reject the null hypothesis; the values for p1 and p2 indicate that there is strong enough evidence
	D.	reject the null hypothesis; the P-value indicates that there is strong enough evidence

3.

Investigators gave caffeine to fruit flies to see if it affected their rest. The four treatments were a control, a low caffeine dose of 1 mg/ml of blood, a medium dose of 3 mg/ml of blood, and a higher caffeine dose of 5 mg/ml of blood. Twelve fruit flies were assigned at random to the four treatments, three to each treatment, and the minutes of rest measured over a 24-hour period were recorded. The data follow.

Treatment

Minutes of rest

Control	450	413	418
Low dose	466	422	435
Medium dose	421	453	419
High dose	364	330	389

Assume the data are four independent SRSs, one from each of the four populations of caffeine levels, and that the distribution of the yields is Normal.

A partial ANOVA table produced by Minitab follows, along with the means and standard deviation of the yields for the four groups.



The null hypothesis for the ANOVA F-test is that the population mean rest is:

	A.	the same for all four levels of caffeine.
	B.	increasing as the caffeine level gets larger.
	C.	decreasing as the caffeine level gets larger.
	D.	largest for the high level of caffeine.

4.

In the United States, there has historically been a strong relationship between smoking and education, with well-educated people less likely to smoke. To examine whether this pattern has changed, a sample of 459 men was selected at random from those who had visited a health center for a routine check-up over the course of the past year. Education is classified into three categories corresponding to the highest level of education achieved, and smoking status is classified into four categories.

Smoking Status

Education	Nonsmoker	Former	Moderate	Heavy	Total
High School	56	54	41	36	187
College	37	43	27	32	139
Graduate	53	28	36	16	133
Total	146	125	104	84	459

This is an r × c table. The number c has value:

	A.	6.
	B.	2.
	C.	4.
	D.	3

Answer 1

1. The degrees of freedom is given by the formula is given by:

, where 1 denotes the sample estimates for poisoned rats and 2 denote the sample estimates for non-poisoned rats. Here n1-n2=6, s1=6.34 and s2= 1.95. Using these values we get df= 5.94. The nearest integer to this is 6.

Thus the correct option is D. 6

2. The p-value of the test is 0.012. Thus the answer is A. accept the null hypothesis

3. A. the same for all four levels of caffeine​​​​​​​

4. c is the number of columns. Thus the answer is D. 3