A species of marine arthropod lives in seawater that contains calcium in a concentration of 32 mmole/kg of water. Thirteen of the animals are collected and the calcium concentrations in their coelomic fluid are found to be 28, 27, 29, 29, 30, 30, 31, 30, 33, 27, 30, 32 and 31 mmole/kg. Test at 5% level of significance appropriate hypothesis to conclude whether members of this species maintain a coelomic calcium concentration less than that of their environment.

A study was conducted to examine the beliefs held by adolescents regarding smoking and weight. Smoking Yes No Underweight 17 97 Overweight 25 142 Appropriate 96 816
Do the data provide sufficient evidence to suggest that weight perception and smoking status are related in adolescents? ( = 0.05
(Given that[pic] =5.991, [pic] = 12.592)

In a study of Margan syndrome, the following severity scores of patients with none and marked dural ectasia were reported
No dural ectasia : 18, 18, 20, 21, 23, 23, 24, 26, 28
Marked dural ectasia : 17, 24, 26, 30, 30, 33, 34, 35
Can we conclude at 5% level of significance, that the mean severity scores differ between the two populations represented in the study?
(Given t15(0.025) = 2.13, t16(0.025) = 2.12, Z0.025 = 1.96)

Two pain-relieving drugs were compared for effectiveness on the basis of length of time elapsing between administration of the drug and cessation of pain. Thirteen patients received drug 1 and 13 received drug 2. The sample variances were 64 and 16 respectively. Test the null hypothesis that the two population variances are equal. Let ( =0.05

Independent simple random samples from two strains of mice used in an experiment yielded the following measurements on plasma glucose levels following a traumatic experience Strain A: 54, 99, 105, 46, 70, 87, 55, 58, 139, 91 Strain B: 93, 91, 93, 150, 80, 104, 128, 83, 88, 95, 94, 97
Do these data provide sufficient evidence to indicate that the mean is larger in the population of Strain A mice than in the population of Strain B mice? Let ( = 0.05. What assumptions are necessary?

In a Greenhouse experiment on wheat, four fertilizer treatments of the soil. The table gives the yield in some suitable unit. Analyze the data to check for the homogeneity of fertilizers.
|Fertilizers |1 |2 |3 |4 |
|1 |21.4 |20.9 |19.6 |17.6 |
|2 |14.2 |13.7 |13.3 |12.0 |
|3 |13.5 |14.0 |12.9 |13.7 |
|4 |13.8 |14.1 |14.2 |12.0 |

Each of a sample of 250 men drawn from a population of suspected joint disease victim was asked which of three symptoms bother him most. The same question was asked of a sample of 300 suspected women joint disease victims. The results are as follows:

Most Bothersome Symptom Men Women

Morning Stiffness 111 102 Nocturnal Pain 59 73 Joint Swelling 80 125

TOTAL 250 300

Do these data provide sufficient evidence to indicate that the two populations are not homogeneous with respect to major symptoms?

In an epidemic of certain disease 92 children contracted the disease. Of these, 41 received no treatment and of these 10 showed after-effects. Of the remainder who did receive treatments, 17 showed after-effects. Test the hypothesis that treatment was not effective.

The following data are weights of food (in kilograms) consumed per day by adult deer collected at different times of the year. Test the null hypothesis that food consumption is the same for all the months tested. Use ( = 0.05 Feb. 4.7 4.9 5.0 4.8 4.7 May 4.6 4.4 4.3 4.4 4.1 4.2 Aug. 4.8 4.7 4.6 4.4 4.7 4.8 Nov. 4.9 5.2 5.4 5.1 5.6

The following are the figures (in thousands) of 3 salesmen in 4 metropolitans for a newly launched Chocolate. Test whether the three salesmen are equally competent. Also test whether the four metropolitans are homogenous in terms of consumption patterns.

|Metropolitan |Delhi |Mumbai |Kolkatta |Chennai |
| | | | | |
|Salesman | | | | |
|Rafeez |11 |5 |9 |10 |
|Manoj |8 |12 |10 |5 |
|Kunal |4 |9 |8 |10 |

(Given that the Sum of squares due to Salesman = 2.667, Sum of squares due to Metropolitan = 2.917 and Total Sum of Squares = 70.917)

In an opinion poll, the respondents are asked to vote either in favor or against a proposition. The following data are obtained on the basis of a random sample of 200 voters. It is intended to examine possible association between age and voting pattern.

| |In favor |Against |
|Young |80 |20 |
|Middle-aged |40 |30 |
|Old |20 |10 |

Six junior managers of a company participated at a management development program (MDP). Their score, with reference to a particular kind of selling skill, before and after the MDP are as follows:

S.No of participant 1 2 3 4 5 6
Score before MDP 40 52 65 43 56 30
Score after MDP 45 60 62 50 55 45
At 5% level of significance, would you conclude that the MDP was effective in enhancing the average selling skill of the participants.

The following table shows the distribution of 140 car drivers according to their ages and the number of accidents made by them in one year.
Age in years
No. ofAccidents 21-30 30-40 40-50 50-60 TOTAL 0 25 30 20 15 90 1 14 8 6 4 32 2 8 5 4 1 18 Total 47 43 30 20 140
Test whether age and the number of accidents made in the year are independent.

A certain company manufacturing house hold articles appointed 4 salesmen [pic] and their monthly sales (lakhs of Rupees) is as follows.

[pic]

A manufacturing company produces screws of a particular size which are put into boxes of 150. On particular day a random sample of such boxes is taken from each of the morning and afternoon production runs. The numbers of defective screws in each sampled box are given in the following table.

| |Number of defectives per box |
|1. literates |
|2. illiterates |
|3. all people. |
|Comment on your results. |

|The following figures gives the prices (Rs) of a certain commodity in a sample of 10 shops each selected at random from City A and City B. |
|City A: 7.41 7.77 7.44 7.40 7.38 7.93 7.58 8.28 7.23 7.52 |
|City B: 7.08 7.49 7.42 7.04 6.9 7.22 7.68 7.74 7.28 7.43 |
|Formally test for the equality of variances of the prices between the two cities at 5% level. |
|Assuming equality of variances construct 95% Confidence interval for the presumed common standard deviation of the prices. |
|Test at the 5% level that the mean price of the commodity in city A is greater than Rs. 7.40. |