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.
Let's evaluate each statement one by one and determine whether they are True or False, providing reasoning for each. --- ### (a) If probability density function of a t-distribution is \[ f(t) = \frac{1}{\pi(1+t^2)}, -\infty
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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.
If the sample values are 3, 5, 2, 7, and 0 then obtain the ML estimate for parameter θ for the following distribution :
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.
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.
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?
. 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 | ||||||||||||||||||