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A manufacturer of alkaline batteries expects
that only 5% of his products are defective.
A random sample of 300 batteries contained
10 defectives. Can we conclude the proportion of
defectives in the entire lot is less than 0.5 at 5%
level of significance ?

The two regression lines between X and Y are
8X - 1OY + 66 = 0, 40X - 18Y = 2x4. The - -
variance of X is 9. Find X, Y, oy , and p.
Explain the method of testing normality by
using chi-squared test. 4x1 0-d0
If Cov (q, Xj) = r. - ,
1J
i j = 1 2, 3, i # j, then
show that

2 2 2 . (ii) rlz + + rI3 5 1 + 2r12r23 rI3
(i) Show that the arithmetic mean of (positive)
regression coefficients is greater than the
correlation coefficient.

(ii) What is the value of the product of
geometric mean of variances and the
geometric mean of regression coefficients ?
Define 'minimum mean square error' and 'best
linear predictor'. Show that they coincide for the
normal distribution.

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