Statistics and Probability Answers

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                                                                                           

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

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

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

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

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

the fraction of defective items in a large lot is ‘p’. to test the null hypothesis h0: p=0.2, one consider the number ‘f’ of defectives in a sample of 8 items and accept the hypothesis if f≤6, and reject the hypothesis otherwise. what is the probability of type-1 error of the test? what is the probability of type-2 error of the test?

The number of items rejected daily by a manufacturer because of defects for the last 30 days are:

20, 21, 8, 17, 22, 19, 18, 19, 14, 17, 11, 6, 21, 25, 4, 19, 9, 12, 16, 16, 10, 28, 24, 6, 21, 20, 25, 5, 17, 8

a) Construct a stem-and-leaf display. What can conclude based on the display? (7 marks)

b) Calculate the mean, median, and mode of the data. (6 marks)

c) Based on the answers in (b), make a conclusion about the skewness of the data. (3 marks)

A study is being conducted on the effect of gas price on the number of miles driven in a given month. Residents in two cities, one on the East Coast and one on the West Coast, are randomly selected and asked to complete a questionnaire on the type of car they drive, the number of miles they live from work, the number of children under 18 in their household, their monthly income, and the number of miles they have driven over the past 30 days.

(a) List the response variable(s) and the type of measurement scale (nominal/ordinal/interval/ratio) associated with each response variable.

(b) Also, state whether this study is an experimental or observational study? Explain in brief the reason for your answer.

4. Assume that the mean life of a particular brand of car battery is normally distributed with a mean of 28 months and a standard variation of 4 months.

(a) for a randomly selected battery of this make, what is the probability that it will last between 30 and 34 months?.

(b) what is the probability that a randomly selected battery of this make will fail within years of date of purchase?.

(c) after what time period will 60% of all batteries of this makes fail?.

1. Hospital records show that of patients suffering

from a chronic disease 75% die of it.

What is the probability that of 6 randomly

selected patient 4 will recover.

2. A die is tossed 3 times. What is the probability of:

a. One five turning up

b. 3 fives turning up

c. No five turning up.

the new drug was administered to 15 patients, the following

drops in systolic blood pressure were registered: 12, 8, 15, 9, 10, 11,

14, 13, 6, 9, 14, 12, 18, 14 and 16 points. Assuming that the drops in

systolic blood pressure are normally distributed.

(a) Construct a 99% confidence interval for the mean drops in blood

pressure.

(b) The manufacturer of a new drug claims that it will lower blood

pressure by 13 points on the average. Is the claim sustained at

the 0.01 level of significance?

a partially destroyed laboratory data, only the equations giving the two lines of regression of x on y and y on x are available and are respectively, 7x-16y + 9 = 0, 5y - 4x-3 = 0. Calculate

the coefficient of correlation, x and y.

The randomly selected 60 shoppers have rated a new bottle design for a popular soft drink. The data are given below. Determine the no. of classes, class width, and the relative frequency of each class to construct the histogram for the given data. Explain the skewness of data based on the histogram. 

34 33 33 29 26 33 28 25 32 33

32 25 27 33 22 27 32 33 32 29

24 30 20 34 31 32 30 35 33 31

32 28 30 31 31 33 29 27 34 31

31 28 33 31 32 28 26 29 32 34

32 30 34 32 30 30 32 31 29 33

Mean life time of a sample of 400 of an product by a company is 1600 hours with a standard deviation of 150 hours. Test the hypothesis that the mean life of the product is more than 1570 hours at 1% level of significance