Question

A random sample of 900 member has a mean 3.4cms. Can it be reasonable regarded as a sample from a large population of mean 3.2cms and S.D 2.3cms?

Answer 1

Answer:

Sample size is 900. The probability we get is 0.915. Hence, we can say that the sample belongs to the population with a probability 0.915 or a confidence level of 91.5%.

Answer 2

Given:

 sample size $n = 900$

  sample mean $\overline{\rm x} = 3.4 cm$

  sample SD $\sigma = 2.3 cm$

Null Hypothesis $H_0$ :$\mu = 3.2cm$

Alternative Hypothesis $H_1 : \mu \neq 3.2cm$

The sample has not been drawn from the population mean $\mu = 3.2 cm$

 and SD $\sigma = 2.3 cm.$

 The level of significance $\alpha = 5$ % $= 0.05$

Teststatistic:

           $Z = \frac{3.4-3.2}{\frac{2.3}{\sqrt{900} } } = \frac{0.2}{0.076}$

                              $= 2.631$

    ∴$Z = 2.631$