Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 416 gram setting. It is believed that the machine is underfilling the bags. A 15 bag sample had a mean of 413 grams with a variance of 729. Assume the population is normally distributed. A level of significance of 0.05 will be used. Specify the type of hypothesis test.

Answer 1

Solution :

= 416

= 413

=729 = 27

n = 15

This is the two tailed test .

The null and alternative hypothesis is

H₀ :   = 416

H_a : 416

Test statistic = z

= ( - ) / / n

= (413- 416) /27 / 15

= -0.43

P (Z < -0.43) = 0.667

P-value = 0.667

= 0.05  

p=0.667 ≥ 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that