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

Explanation:

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

`z=\frac{\overline{x}-\mu}{(\sigma)/(√(n))}`

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

As per given,

`z=(55.82-56)/((0.77)/(√(49)))\\\\ z=(-0.18)/((0.77)/(7))\\\\z=(-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