ISS (Statistical Services) Statistics Paper IV: Questions 42 - 46 of 92

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Question 42

Describe in Detail

Essay▾

Compute the crude and standardized death rates of the populations A and B, regarding A as standard population, from the following data:

Showing Table of the Crude and Standardized Death Rates of the Populations a and B
Age groups

(years)

AB
PopulationDeathsPopulationDeaths
Under 102000060012000372
10 - 201200024030000660
20 - 40500001250620001612
40 - 6030000105015000525
Above 60100005003000180

Explanation

From the given data, the crude death rate for any population is

For population A

For population B

The standardized death rate is

Where pxs = population of standard group of x and Dx = Age specific death rate of group x.

Showing Table of Standardized Death Rate for Population a and B
Age groupsStandard population (Px)Dx for population ADx for population BPx ⚹ Dx for APx ⚹ Dx for B

… (82 more words) …

Question 43

Describe in Detail

Essay▾

Following data gives the diameter of the rings manufactured by a company. Obtain the Control limits for R-chart.

Sample is Given with Observations
Sample No.Observations
15.025.014.944.994.96
25.015.035.074.954.96
34.995.004.934.924.99
45.034.915.014.984.89
54.954.925.035.055.01
64.975.065.064.965.03
75.055.015.104.964.99
85.095.105.004.995.08
95.145.104.995.085.09
105.014.985.085.074.99

Explanation

From the tables, for n = 10, we have , ,

Control limits for :

5.01 + 0.0354 = 5.045

And 5.01 + 0.0354 = 4.97

Sample is Given with Observations – X Bar Chart

chart shows the process is out of control.

Control limits for R chart :

= (0.223) (0.115) = 0.0256

Sample is Given with Observations – R Chart

R chart shows the process is under control.

… (15 more words) …

Question 44

Appeared in Year: 2013

Describe in Detail

Essay▾

For a PBIB design with parameters , b, r, k, , show that

Explanation

A PBIB design with m associate classes based on the association scheme is an arrangement of treatments into b blocks such that

(i) Each block contains k distinct treatments (k <

(ii) Each treatment occurs in r blocks

(iii) Any two treatments, which are ith associates occur together in blocks (i = 1,2, . . , m) are called the parameters of the PBIB …

… (58 more words) …

Question 45

Appeared in Year: 2012

Describe in Detail

Essay▾

Discus symmetrical BIBD. For an SBIBD , under usual notations, show that

=

Explanation

Symmetrical BIBD:

A BIBD is said to be symmetric if b = υ and r = k.

υ, r, b, k and λ are called the parameters of the BIBD

υ = number of varities or treatments

b = number of blocks

r = number of replicates for each treatment

k = block size

λ = number of blocks in which any pair of treatments occurs together

Proof: =

Let N be the incident matrix of a SBIB…

… (79 more words) …

Question 46

Edit

Appeared in Year: 2015

Describe in Detail

Essay▾

Discuss how you would proceed with the analysis if data on one plot is missing in a Latin Square design.

Explanation

To analysis the data of a Latin square design having missing values, we first estimate the missing value by minimizing the error mean square and the rest missing values by guess estimate which is generally the mean of all available values. The estimated value of x is obtain by to minimize the error variance, differentiate the expression for it with…

… (200 more words) …