Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 445 gram setting. It is believed that the machine is underfilling the bags. A 12 bag sample had a mean of 442 grams with a standard deviation of 20. A level of significance of 0.05 will be used. Assume the population distribution is approximately normal. State the null and alternative hypotheses.

Answer 1

The null hypothesis is
`H_o : \mu = 445`

The alternative hypothesis
`H_a : \mu < 445` (This is the original claim[ It is believed that the machine is under filling the bags] )

Explanation:

From the question we are told that

The population mean is
`\mu = 445 \ g`

The sample size is
`n = 12`

The sample mean is
`\= x = 442 \ g`

The standard deviation is
`\sigma = 20`

The level of significance is
`\alpha = 0.05`

The null hypothesis is
`H_o : \mu = 445`

The alternative hypothesis
`H_a : \mu < 445` (This is the original claim )