Question

The process that produces Sonora Bars (a type of candy) is intended to produce bars with a mean weight of 56 gram. The process standard deviation is known to be 0.77 gram. A random sample of 49 candy bars yields a mean weight of 55.82 gram. Find the test statistic to see whether the candy bars are smaller than they are supposed to be.

Answer 1

Answer: z= -1.636

Step-by-step explanation:

When population standard deviation is known, then the test statistic is given by :-

$z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

, where $\overline{x}$ = sample mean, $\mu$ = population mean, n=sample size , $\sigma$ = standard deviation

As per given,

$z=\dfrac{55.82-56}{\dfrac{0.77}{\sqrt{49}}}\\\\ z=\dfrac{-0.18}{\dfrac{0.77}{7}}\\\\z=\dfrac{-0.18}{0.11}\\\\z=-1.636$

Hence, the e test statistic to see whether the candy bars are smaller than they are supposed to be : z= -1.636