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STATS / MMS-I /INFERENTIAL ANALYSIS

Assignment to be submitted groupwise on 10 the November 2010

Q1 a) Differentiate between following,

1. Parameter and statistic.

2. Level of significance and level of confidence.3. Null and Alternate hypothesis.

4. Type-I and type-II error.

5. One-tailed and two-tailed test of hypothesis

6. Testing of hypothesis and estimation.7. Point estimate and interval estimate.

8. Parametric and non-parametric test of hypothesis

9. Z-test and t-test of hypothesis.10. Test of goodness of fit and test of independence, under chi-square testing

b) Explain the hypothesis testing procedure with large sample, to examine the null

hypothesisH0: Mean for proportion for population 1 = Mean for proportion for population 2

Write assumptions you made wherever required.

Q2) To study performance of three types of advertising themes in 3 different regions

for a recently developed medicine, the following sales (in Rs lakhs) record is available

Regions Ad. theme A Ad. theme B Ad. theme C

Punjab 59 57 69

Maharashatra 51 54 70

Tami nadu 56 48 58

Perform two-way ANOVA, using 5% level of significance, to test

whether there is significant difference in sales due to difference in

advertising theme and region.(Critical value of F at 5 % level of significance

for degrees of freedom (2, 4) is 6.94)

Q3) In a study of a newly developed electronic toy, following table was obtained, for

sales in 9 shops in different malls, before and after a special promotional scheme

shop 1 2 3 4 5 6 7 8 9

Sales ( in units per day )

before

22 20 17 12 24 32 18 26 27

Sales ( in units per day )

after

24 23 22 17 28 32 22 27 30

Using an appropriate t test at 5 % level of significance, can we conclude thatspecial promotional scheme was a success?

(Critical value for degrees of freedom 8 for one-tailed test is = 1.860)

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Q4 While checking quality of product, one particular dimension was varying due to

changes in machine setting. The population mean was expected to be 50 mm with

standard deviation of 2.5 mm. A random sample of 50 units of this product, checked byquality inspector gave mean of 48.5 mm. Test whether the process mean is guarded

against decreasing value, at 5% level of significance.

Q5 A sociologist selected a random sample of 180 couples from a large population of

married couples. The attitudes of husband and wife towards womens liberation were

then ascertained. Following are the data on husbands and wifes responses,Husband

Wife Favorable Indifferent Against

Favorable 36 29 9

Indifferent 18 45 7

Against 10 9 17

Using an appropriate chi-square test, examine whether opinions of wives

are independent of husbands. Test at 5 % level of significance

Q6 In an experiment on pea-breeding, researcher obtained following

frequencies of seeds

Round and yellow 315, Round and green 108,Wrinkled and green 32. Wrinkled and yellow 101,

According to theory of heredity, the numbers should be in the proportion 9:3:3:1.

Is there any evidence to doubt the theory at 5% level of significance?

Q7 A study of 320 families with 5 children each, shows following details,

Boys 5 4 3 2 1 0

Girls 0 1 2 3 4 5No. of

families

14 56 110 88 40 12

Use an appropriate chi-square test, to check these results are consistent with

hypothesis boys are girls are having equal probability. Test at 5% level of

significance.(Use binomial distribution to calculate expected frequencies)

Q8 Out of a random sample of 900 days taken from weather records for a certaindistrict, 100 days are found to be foggy. What are limits for number of foggy days in the

district with confidence level of 99.73%?