A random sample of nine college students yielded the following data concerning the number of hours per day each student spent in using mobile phone:
5, 2, 7, 5.5, 3.5, 4, 5, 4.5, 4
Estimate the average number of hours per day spent in using mobile phone by the college students.
To estimate the average number of hours per day spent using a mobile phone, ___ _____ ________ ________ ________.
____ _______ __________ __________ ___ ______ _______ ___.
____ ______ ___ ______ _______.
________ _____ ___ ____ ___ __________ _______ ___ _________ _________.
__________ _______ ________ __________ ________ ______ _____ ________ ____ ________ ___.
_______ ______ ____ _______ _________ __________.
________ ________ __________ _________ __________.
______ _______ ___ _____ _____ ____ _______ ____ _________ _________ ______.
__________ _____ __________ _____ ______ _________ ___ _____ ________ _______.
____.
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In a city, 36 out of a random sample of 500 men were found to drinkers at a certain date. After the heavy increase in tax on intoxicants, another sample of 100 men in the same city included 6 drinkers. Do you feel that the observed proportion of drinkers decreasing significantly at 1%level?
Which non-parametric test is used for testing the null hypothesis if it is known that the scores of the employees before and after the training programme do not follow the normal distribution but the distribution of the differences of scores before and after the training is symmetrical about its median? Conduct the test at 1% level of significance and conclude the result.
A company is trying to improve the work efficiency of its employees. It has organized a special training programme for all employees. In order to assess the effectiveness of the training programme, the company has selected 10 employees randomly and administered a well-structured questionnaire. The scores (out of 100) obtained by the employees are given in the following table:
| S. No | Before Training | After Training |
| 1 | 60 | 68 |
| 2 | 62 | 70 |
| 3 | 67 | 80 |
| 4 | 64 | 74 |
| 5 | 66 | 66 |
| 6 | 63 | 72 |
| 7 | 69 | 84 |
| 8 | 63 | 60 |
| 9 | 60 | 65 |
| 10 | 62 | 90 |
The following data relate to the number of items produced per shift followed normal distribution by two workers Rahul and Ramesh for a number of days:
| Rahul | 19 | 22 | 24 | 27 | 24 | 18 | 20 | 19 | 25 | |||||||||||
| Ramesh | 26 | 37 | 40 | 35 | 30 | 40 | 26 | 30 | 35 | 45 | ||||||||||
. Complete the following table:
| S. No. | Test for | Name of the Test | Null and Alternative Hypotheses | Test Statistic | Assumptions for Applying the Test | Decision Rule (in short) | |||||||||||||
| 1 | Population mean when population variation is known | ||||||||||||||||||
| 2 | Population mean when population variation is unknown | ||||||||||||||||||
| 3 | Population proportion | ||||||||||||||||||
| 4 | Difference of two population means | ||||||||||||||||||
| 5 | Two population standard deviation | ||||||||||||||||||
| 6 | Difference of two population proportion | ||||||||||||||||||
| 7 | Independence of two attributes | ||||||||||||||||||
State whether the following statements are True or False. Give reason in support of your answer.
a) If probability density function of a t-distribution is
then degrees of freedom of the distribution will be 1.
b) If T1 and T2 are two estimators of an parameter θ such that Var(T1) = 1/2n and
Var(T2) = 2/n then T1 is more efficient than T2.
c) If the probability of non rejection of H0 when H1 is true is 0.4 then power of the test
will be 0.6.
d) The Wilcoxon signed-rank test is more powerful than the sign test.
e) The t-test is used for testing the independence of two attributes.
A sample of 100 tyres is taken from a lot. The mean life of the tyres selected is the sample is found to be 40,000 kms with a standard deviation of 3200 kms. Is it reasonable to suppose the mean life of tyres in the lot as 41,000 kms at 5% level of significance? Also establish 95% confidence limits within which the mean life of tyres in the lot is expected to lie.