Statistics and Probability Answers

. A clinical trial to assess the effectiveness of the HPV (human papilloma virus) vaccine for preventing cervical cancer in women found a Relative Risk of 0.10 with a 95% Confidence Interval of 0.05 to 0.15. Which of the following statements is the correct interpretation of the study findings?

a)  Women who were vaccinated against HPV are 10 times as likely to develop cervical cancer compared to those who were not vaccinated, and this difference is statistically significant.

b)  Women with cervical cancer are 10 times as likely to have been vaccinated against HPV compared to those who were not vaccinated, but this difference is not statistically significant.

c)Women who were vaccinated against HPV have a <u>90% decrease</u> in risk of developing cervical cancer compared to those who were not vaccinated, and this difference is statistically significant.

d)  Women who were vaccinated against HPV have a 90% increase in risk of developing cervical cancer compared to those who were not vaccinated, and this difference is statistically significant.

In a certain Algebra 2 class of 29 students, 7 of them play basketball and 14 of them play baseball. There are 10 students who play neither sport. What is the probability that a student chosen randomly from the class plays basketball or baseball?

Mr Mukonda’s perfomance of his 170 Biostatistics class of students

is given in an incomplete distribution below.

CLASS     FREQUENCY

0-10         12

10-20        21

20-30        f1

30-40        40

40-50        f2

50-60        26

60-70        18

(a) If the median is 35. Find the missing frequencies f1 and f2.

(b) From Rusangu University passing mark policy(40%), explain if the above results are normally distributed

A parking lot has 10 parking spaces arranged in a row. There are 7 cars parked. Assume that each car owner has picked at a random a parking place among the spaces available. Specify an appropriate sample space and determine the probability that the three empty places are adjacent to each other.

The chemical of COVID 19 vaccine is non-toxic to humans. Government regulations dictate that for any production process involving COVID 19 vaccine, the water in the output of the process must not exceed 7950 parts per million (ppm) of COVID 19 vaccine. For a particular process of concern, the water sample was collected by a manufacturer ‘58’ times randomly and the sample average x^- was 7960ppm. It is known from historical data that the standard deviation σ is 100 ppm. What is the probability that the sample average in this experiment would exceed the government limit if the population mean is equal to the limit? Use the Central Limit Theorem.

A mathematics placement test is given to all entering freshmen at Eastern

University. n = 58,x ̄= 4,y ̄ = 12, ∑ⁿ_i=1 x_i² =232, ∑ⁿ_i=1 x_iy_i =318. , .Fit a simple

linear regression model between x and y.

3- Refer the given output and answer the following questions; [5 Marks] a) Identify which statistical analyses have been performed? b) Interpret each of the given tables. Table 1: Statistical Analysis Variables Beta Sig VIF Organizational Culture 0.253 0.000 1.124 Job Stress -0.101 0.078 3.542 Intrinsic Motivation 1.213 0.005 12.389 Dependent variable is employee performance Table 2: Statistical Analysis Variables Composite Reliability AVE Attitude 0.78 0.23 Behaviour 0.52 0.78 Consumption 0.92 0.50 Overall 0.98 0.44

The hospitalization period, in days, for patients following treatment for a certain

type of virus X, where X has the density function f(x) = 4/{π(x² +1)}

, 0<x <58. Find

the expected value of X. that a person is hospitalized following treatment for this

disorder.

Following is the data related to the daily production of the two factories of same product located in two different states.

Factory

Daily Production

Factory 1

66

66

73

83

74

73

73

69

82

71

73

66

67

80

79

78

Factory 2

66

63

71

65

65

67

57

48

71

73

68

58

62

81

60

62

72

72

57

77

68

a.     Calculate the following                                                                                              [2]

Daily Production of Factory 1

Daily Production of Factory 1

Sample Size

Degree of freedom

Mean

Variance

Standard Deviation

b.    Calculate the ratio of two variances and test the equality of the variances and comments.[1]

c.     Calculate the value of pool standard deviation (S_p), degree of freedom in the light of part “b” and SED                                                                                                                       [1]

d.    Write the null and alternative hypothesis for comparing the production of two factories. [1]

e.     Calculate the critical values “t_tab”, and t_cal                                                                     [1]

Write the conclusion for the null hypothesis of part “d”     

1)     In a frequency distribution of 100 families given below the number of families corresponding to expenditure groups 20-40 and 60-80 are missing from the table. However, the median is known to be 50.

 Expenditure group

0-20

20-40

40-60

60-80

80-100

No. of families

14

f2

27

f4

15

a)         Find the missing frequencies.

b)        Find mean, mode, variance, standard deviation, range, mean deviation for mean and median