Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 404 gram setting. It is believed that the machine is underfilling the bags. A 43 bag sample had a mean of 400 grams. Assume the population standard deviation is known to be 18. 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 :   = 404

H_a : < 404

Test statistic = z

= ( - ) / / n

= (400 - 404) / 18 / 43

= -1.46

P(z < -1.46) = 0.0721

P-value = 0.0721

= 0.1

P-value <

Reject the null hypothesis .