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

Solution,

The null and alternative hypothesis is ,

H0 :   = 420

Ha : < 420

= 413

2 = 676

= 2 = 676 = 26

n = 49

Test statistic = z =

= ( - ) / / n

= (413 - 420) / 26 / 49

Test statistic = z = -1.88

This is the left tailed test .

P (Z < -1.88)

P-value = 0.0301

= 0.1

P-value <

Reject the null hypothes