Statistics and Probability Answers

The numbers 3.2, 5.8, 7.9 and 4.5 have frequencies Y, (Y + 2), (Y - 3) and (Y + 6), respectively. If the arithmetic mean is 4.876, find the value of Y and write the whole series.

The value of Spearman's rank correlation coefficient of a set of non-repeating values was found to be 2/3. The sum of the squares of difference between the corresponding ranks was 55. Find the number of pairs.

Given the following data: r12 = 0' 8 , r13 = 0.6 and r23= 0.4 then find

(i) r12.3

(ii) r13.2

(iii) r23.1

(iv) R1.23

In a statistical study relating to the prices (in T) of two shares, X and Y, the following two regression lines were found as 8X - 10Y + 70 = 0 and 20X - 9Y - 65 = 0. The standard deviation of X = 3, then find (i) the values of X and Y, (ii) r(X, Y), and (iii) standard deviation of Y.

An investigation of 23713 households was made in an urban and rural mixed locality. Of these 1618 were farmers, 2015 well to do and 770 families were having at least one graduate. Of these graduate families 335 were those of farmers and 428 were well to do; also 587 well to do families were those of farmers and out of them only 156 were having at least one graduate. Obtain all the ultimate class frequencies.

If a finite population has four elements: 6, 1, 3, 2.

(a) How many different samples of size n = 2 can be selected from this population if you sample without replacement?

(b) List all possible samples of size n = 2.

(c) Compute the sample mean for each of the samples given in part b.

(d) Find the sampling distribution of x.

(e) Compute standard error.

(f) If all four population values are equally likely, calculate the value of the population mean μ . Do any of the samples listed in part (b) produce a value of x exactly equal to μ ?

Give reason whether the following statements are True or False.

(a) If the probability of non rejection of H0 when H1 is true is 0.4 then power of the test will be 0.6.

(b) If T1 and T2 are two estimators of the parameter θ such that Var(T1) = 1/n and Var(T2) = n then T1 is more efficient than T2.

(c) A 95% confidence interval is smaller than 99% confidence interval.

(d) If the level of significance is the same, the area of the rejection region in a two-tailed test is less than that in a one-tailed test.

(e) Non parametric tests are more powerful than the parametric tests.

Samples of three cards are drawn at random

from a population of eight cards numbered

from 1 to 8.

1. Construct a histogram of the sampling

distribution of the means.

The numbers of workers of a new fast food restaurant with seven outlets are 9 10 9 11 13 12 and 8 compute the population mean population variance and population standard deviation use the long method