Question

5.26  What is wrong? Explain what is wrong in each of the following statements.

1. (a) The central limit theorem states that for large n, the population mean μ is approximately Normal.

2. (b) For large n, the distribution of observed values will be approximately Normal.

3. (c) For sufficiently large n, the 68–95–99.7 rule says that x¯x¯ should be within μ ± 2σ about 95% of the time.

4. (d) As long as the sample size n is less than half the population size N, the standard deviation of x¯x¯ is σ/n−−√σ/n.

Answer 1

Answer:

a)

As far as possible hypothesis expresses that for enormous n , inspecting circulation of mean x-is around Normal and not µ which is a fixed worth and doesn't follow any likelihood appropriation as it is fixed worth.

b)

Here as we realize that watched qualities follow their populace dispersion which can be any dissemination. For huge example size n, conveyance of test mean follows typical circulation and not appropriation of watched esteems.

c)

The 68-95-99.7 principle says that a xbar ought to be inside µ ± 2σx about 95% of the time ,where σx is standard blunder of mean and not populace standard deviation σ .

d)

Here it isn't the situation for each example of size i.e.,n a bit much 50% of the N will have standard deviation xbar to be σ/sqrt(n).