Statistics and Probability Answers

True or False. Justify
There is no difference between type I error and level of significance.

true or false? Justify.
If firm A has 5 employees with median salary Rs. 11,000 and firm B has 5 employees with median salary Rs. 15,000, then after merging the median salary of the employees will be Rs. 13,000.

Ten individuals are chosen at random, from a normal population and their (5)
eights (in kg) are found to be 63, 63, 66, 67, 68, 69, 70, 70, 71 and 71. In the
light of this data set, test the claim that the mean weight in population is 66 kg
at 5% level of significance.
[The following tά values are given]
degree of
freedom ά = 0.05 ά = 0.025
9 1.83 2.26
10 1.81 2.23

In an air pollution study, a random sample of 200 households was selected from each of 2 communities. A respondent in each house was asked whether or not anyone in the house was bothered by air pollution. The responses are tabulated below:
Community Yes No Total
I 43 157 200
II 81 119 200
Total 124 276 400
Can the researchers conclude that the 2 communities are bothered differently by
air pollution? (a = 0.05)

Following are the marks obtained by 49 students in Maths paper in a class with
minimum marks 50:
Mark
Group 5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45

Frequency 5 6 15 10 5 4 2 2
Draw a histogram of marks obtained and find the mode from the histogram.

A population of size 500 is divided into 4 strata. The following table gives the (5)
data on size and standard deviation of each stratum.
STRATA
I II III IV
Size 100 150 150 100
S.D. 5 8 7 10
A stratified random sample of size 100 is to be drawn from the population.
Determine the size of samples from each of these strata for:
i) proportional allocation
ii) Neyman’s optimal allocation

The distribution of blood groups in a city is:
A : 41%; AB : 4%; B : 9%; O : 46%
An individual injured in a car accident is brought into an emergency room of
the hospital
i) What is the probability that the individual belong to blood-group type A
or B or AB?
ii) Describe the sample space and events in the above question.

The results of a survey regarding radio listeners preference for different types (5)
of music are given in the following table with listeners classified by age group.
Test at 5% level of significance whether type of music is dependent on the age
group.
Age Group
Type of Music 19-25 26-35 Above 36
Preferred
National Music 60 60 30
Foreign Music 190 264 96
Indifferent 50 76 74

The average hourly wage of a sample of 150 workers in plant A was $2.56 with a standard deviation of $1.00. The average hourly wage of a sample of 200 workers in plant B was $2.87 with a standard deviation of $1.20.
Write a suitable hypothesis to test whether the wages are comparable and test it.

Apply the simple exponential smoothing procedure to forecast the following data.
Take W = 0.1
Year 2001 2002 2003 2004 2005
No. of Schools 5 3 4 6 5