Answer: z= -1.636
Step-by-step explanation:
When population standard deviation is known, then the test statistic is given by :-
[tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
, where [tex]\overline{x}[/tex] = sample mean, [tex]\mu[/tex] = population mean, n=sample size , [tex]\sigma[/tex] = standard deviation
As per given,
[tex]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[/tex]
Hence, the e test statistic to see whether the candy bars are smaller than they are supposed to be : z= -1.636
