Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 420 gram setting. It is believed that the machine is underfilling the bags. A 49 bag sample had a mean of 413 grams. Assume the population variance is known to be 676 . A level of significance of 0.1 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.

Answer 1

The value is
`p-value = 0.0297`

Explanation:

From the question we are told that

The population mean is
`\mu = 420 \ g`

The The sample size is
`n = 49`

The sample mean is
`\= x = 413 \ g`

The population variance is
`\sigma^2 = 676`

Generally the population standard deviation is mathematically represented as

`\sigma = √(\sigma^2 )`

`\sigma = √(676)`

`\sigma = 26`

The null hypothesis is
`H_o : \mu = 420 \ g`

The alternative hypothesis is
`H_a : \mu < 420 \ g`

Generally the test statistics is mathematically represented as

`z = ( \= x - \mu )/( ( \sigma )/(√(n) ) )`

=>
`z= ( 413 - 420 )/( ( 26 )/(√(49) ) )`

=>
`z = -1.884`

The p-value is obtained from the z-table table and the value is

`p-value = P(Z < -1.885) = 0.029715`

`p-value = 0.0297`