Answer to Question #188270 in Statistics and Probability for padma raga. A

Question

A sample of 900 items is found to have a mean of 3.47 cm. Write down the R programming code to test whether it can be reasonably regarded as a simple sample from a population with mean 3.23 cm and SD 2.31 cm at 99% level of confidence.

Answer 1

$H_0 : \mu = 3.23 \\ H_1 : \mu ≠ 3.23 \\ \bar{x} = 3.47 \\ \sigma = 2.31 \\ n = 900$

The test statistic:

$z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} \\ z = \frac{3.47 -3.23}{2.31 / \sqrt{900}} \\ z = 3.11$

R programming code:

Calculated $z>z_{alpha}$ , so H₀ is rejected.