Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 447 gram setting. It is believed that the machine is underfilling the bags. A 31 bag sample had a mean of 439 grams. Assume the population variance is known to be 900. 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 :

This is the left tailed test,  

The null and alternative hypothesis is ,

H₀ :   = 447

H_a : < 447

Test statistic = z

= ( - ) / / n

= (439 - 447) / 30 / 31

Test statistic = z = -1.48

P(Z < -1.48)

P-value = 0.0694

0.05 < P-value < 0.10

= 0.1

P-value <

Reject the null hypothesis .