Question 1

a)Assuming a population of 4 pots ( ) and we measure the number of flowers seeds that germinated ( ) after a fixed time, obtaining:

1-The population's mean and variance

2-The mean and the variance of the sampling distribution of for n=2 with replacement are:

3-Verifying the relation between the mean and variance of the population , and the mean and variance of the sampling distribution of the sample mean.

b)A population of 6000 elements, with mean 50 and variance 36. A sample of size 85 elements without replacements. Thus:

4-

a)0.59 b)25 c) 50d)1.7

5-

a) b) c)d)

6-Can we ignore the correction coefficient ?

a)Yesb) Noc) we can't decide

7-Why?

a) b) c) d)

8-Can we apply the central limit theorem?

a)Yes, because n small and Normal distribution

b)Yes, because n large and not Normal distribution

c)No, because n small and not Normal distribution

d)No, because n large and Normal distribution

9-If we can apply the central limit theorem, then the distribution of is:

a) b) c) d)

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Question 2

Use the computer's results as possible as to answer the following questions:

In a sample of 71 cases of food- poisoning in Saudi Arabia, we found that 38.8% of the cases had a public restaurant as the source of food- poisoning.

A)To find 90% confidence interval for the proportion of food poisoning cases:

10-The confidence interval formula is:

11- The confidence interval is:

12-if we assume that the true proportion is 45% , then the sample size needed to have 90% confidence interval within 0.02 is

a)1765b)1675c)1674.35d)1765.35

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B) In a study of a surgical procedure used to decrease the amount of food that person can eat. A sample of 10 persons measures their weights before and after on e year of the surgery, we obtain the following data:

Before / 148 / 154 / 107 / 119 / 102 / 137 / 122 / 114 / 140 / 117
After / 78 / 133 / 80 / 70 / 70 / 63 / 81 / 60 / 85 / 120

Find 95% confidence interval for the difference in the average weight before and after surgery.

13-Data is:

14-The confidence interval formula is:

15-The confidence interval is:

Question 3

If we have the data of the old ages and the IQ test degree in the following table:

Age(x) / 76 / 68 / 71 / 56 / 65 / 53 / 43 / 45
IQ(y) / 65 / 78 / 82 / 87 / 91 / 100 / 100 / 116

16-

17-

18-

19-

20-

21-

22-

23-The regression equation of y on x is:

24-If a person is50 years old, then the IQ test degree is:

25-The Person coefficient value is:

26-The person coefficient value means that the relation is:

27-The determination coefficient value is:

28-The determination coefficient value means that:

a)79.9% of variation in IQ grade can be explained by the variation in age

b)0.799% of variation in IQ grade can be explained by the variation in age

c)89.4 % of variation in IQ grade can be explained by the variation in age

d)0.894 % of variation in IQ grade can be explained by the variation in age

Question 4

Suppose we measure the strength of the shell of an egg(قوة قشرة البيضة). For a sample of white eggs and obtains the followingfrequencies:

Levels of strength
Weak / Moderate / Strong / Total
42 / 63 / 45 / 150

Test if the levels of strength of white egg shells occur with equal proportions at .

29-The hypothesis are:

30-The test statistic is:

31-The test statistic value is:

32-The table value is:

33-The decision is

a)Rejectb) acceptc) we can't decide

Question 5

If some researchers are interested in knowing the effect of water stress on the protein content of wheat. They chose 6 local varieties of Saudi wheat for experiment and it is assumed that there is no interaction between the water stress levels and the wheat varieties on the protein content.

Water stress levels
Varity of Wheat / A / B / C
1 / 19.2 / 19.1 / 20.6
2 / 19 / 21.4 / 21.8
3 / 19.1 / 21.1 / 20.6
4 / 19 / 19.7 / 20.4
5 / 19 / 19.1 / 19.7
6 / 19.7 / 21.7 / 21.9

Use the computer's results to test whether there is a difference in the effects of water stress levels on the average protein content at .

34-The variable is:

a)Water stress levels b) varieties of wheat c) protein content d) none of these

35- The treatments is:

a)Water stress levels b) varieties of wheat c) protein content d) none of these

36-

a)3 b) 6 c) 18 d) 17

37- the hypothesis are:

38- the test statistic is:

a) b) c) d)

39- the test statistic value is:

40- the table value is:

41- the decision is:

a)Rejectb) acceptc) we can't decide

Question 6

(use the computer's results)

A)If we have two independent samples of students (males and females) in KSU for grade of 105 STAT course, as follows:

Females / B / B+ / A+ / D / C+ / A / F / D+ / C / F
Males / A / C+ / D / D+ / F / A+ / B+ / B / A+ / C+

Is the median of grades for females is greater than the median of grades for males at.

42- the hypothesis are:

43- the test statistic is:

44- the test statistic value is:

45- the table value is:

46- the decision is:

a)Rejectb) acceptc) we can't decide

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B) If we want to calculate a correlation coefficient for the previous grades in the table, then:

47- the suitable correlation coefficient is :

a) b) c) d)

48- the value of the correlation coefficient is :

49- the relation between the two grades is :

a)positive moderate b) negative moderate c) positive weakd)no relation

Question 7

A)Suppose we measure the time needed to cool victims of heat stroke (ضربة شمس) during Hajj to Makkah ( in minutes). For a sample of heat stroke victims is given by:

45 20 15 29 6775 35 110 27 4052 33 18 21

Use the sign test to decide if the median of cooling time is less than 50 minutes at

50- the variable is:

a)victims of heat stroke

b) the time of cooling

c)heat stroke during Hajj

d) none of these

51- the hypothesis are:

a) b) c) d)

52- the test statistic is:

a) b) c)d)e)

53- the test statistic value is:

54- the table value is:

55- the decision is:

a)Rejectb) acceptc) we can't decide

B) assuming that the population is normally distributed, thus :

56-The 90% confidence interval formula for the mean of cooling time is:

a) b) c) d) none of these

57- The confidence interval is:

C) Test whether the mean of cooling time is greater than 50 at.thus:

58- the hypothesis are:

a) b) c) d)

59- the test statistic is:

a) b) c)d) e)

60- the test statistic value is:

61- the table value is:

62- the decision is:

a)Rejectb) acceptc) we can't decide

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D) To find the confidence interval for the standard deviation of cooling time at ,

63- the confidence interval formula is:

64- the confidence interval is:

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