From a population with mean 1056, a sample of 400 with sample mean 910 is taken. Then value of test statistic is (\(\sigma = 400\)):
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → −7.3
The population standard deviation is known and the sample is large, so the test statistic is
\(\displaystyle z = \frac{\bar{x}-\mu}{\sigma/\sqrt{n}}\)
Here \(\bar{x} = 910\), \(\mu = 1056\), \(\sigma = 400\), n = 400:
\(\displaystyle \frac{\sigma}{\sqrt{n}} = \frac{400}{20} = 20\)
\(\displaystyle z = \frac{910-1056}{20} = \frac{-146}{20} = -7.3\)