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Statement I A hypothesis test for comparing the variances of two independent populations with the help of variances of two small samples is known as chi-square test.<br>Statement II To test the hypothesis that the population standard deviation has a specific value on the basis of the values of sample standard deviation of small sized sample, F-test isrelevant.

Correct Answer: Both statements are incorrect

Statement I A sampling distribution of mean, prepared on the basis of small sized samples from a population which is not normally distributed, is not normally distributed.
Statement II To test the significance of the difference between means of two small sized samples when the parameter values of the standard deviations are given, Z-test can be applied.

A researcher conduct a hypothesis test and observes values from sample mean and sample standard deviation when n = 25, that do not lead to rejection of null hypothesis. He calculates the p value as 0.0667. What will happen to the p value if he observes the same sample mean and standard deviation for a sample > 25?

A researcher wants to test the significance of the difference between the average performance of the two small sized samples when the information of the population standard deviation is not available, which one of the following hypothesis-testing is suitably used?

Statement I The product of coefficient of correlation, standard deviation of variable 'X' and Standard deviation of variable 'Y' gives the measure of covariance between X and Y variables.
Statement II The product of coefficient of correlation between X and Y variables and the ratio between standard deviation of X variable to standard deviation of Y variable measures the slope of the regression line of X on Y variable.

Direction : Two statements I and II are given. These statement may be either independent causes or may be effects of independent causes or a common cause. One of these statements may be the effect of the other statements. Read both the statements and decide which of the following answer choice correctly depicts the relationship between these two statements. Mark answer :

I. The car manufacturing companies have recently increased the prices of mid-sized cars.
II. The Government recently increased the duty on mid-sized cars.

Assertion (A): A reasonably sized sample drawn randomly from large sized population contains almost all the characteristics which exist in the population.
Reason (R): The theory of sampling is based on the two important laws of statistics, viz law of statistical regularity and law of inertia of large numbers.

Statement I When a null hypothesis is true but as per the hypothesis testing, it is rejected; it is known as Type II error in hypothesis testing.
Statement II For testing the significance of the differences among the performance of more than two sample groups when the data are non-parametric, Kruskal-Wallis (H) test is appropriate.

Statement I Both the probable error and standard error of the coefficient of correlation are different.
Statement II When a sampling distribution of mean is prepared by taking small sized samples from a normally distributed population, the distribution takes the shape of normal distribution.

A student was studying primate uterine thickness. She had 3 samples of uterine tissues. The thickness in mm for the samples are as follows: Sample A – 4 mm, Sample B – 10 mm, Sample C – 1 mm Given the knowledge of menstrual cycle in humans, what phases do you think each sample belongs to?

In two large populations there are 35 and 30 per cent of fair haired people. Will the differ ence disappear at 5% level of significance, if samples of 1500 and 1000 are respectively taken from the two populations?