The blood cholesterol levels of a population of workers have mean 202 mg/dl and standard deviation 14 mg/dl. If a sample of 36 workers is selected from the population and sample mean is calculated then find
i) mean and standard error of the sampling distribution of the mean.
ii) approximate the probability that the sample mean of their blood cholesterol levels will lie between 198 mg/dl and 206 mg/dl.
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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 |
In a locality, 100 persons were randomly selected and asked about their educational achievements. The results were as follows:
| Sex | Education | Total | ||||||||||
| Middle | High School | College | ||||||||||
| Male Female | 12 22 | 13 13 | 25 15 | 50 50 | ||||||||
| Total | 34 | 26 | 40 | 100 | ||||||||
The blood cholesterol levels of a population of workers have mean 202 mg/dl and standard deviation 14 mg/dl. If a sample of 36 workers is selected from the population and sample mean is calculated then find
i) mean and standard error of the sampling distribution of the mean.
ii) approximate the probability that the sample mean of their blood cholesterol levels will lie between 198 mg/dl and 206 mg/dl.
If the sample values are 3, 5, 2, 7, and 0 then obtain the ML estimate for parameter θ for the following distribution :
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.
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.
. 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 | ||||||||||||||||||