Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 433 gram setting. It is believed that the machine is underfilling the bags. A 42 bag sample had a mean of 425 grams. Assume the population variance is known to be 625. A level of significance of 0.05 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 :

= 433

=425

2 = 625

=25

n = 42

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 433

Ha :     433

Test statistic = z

= ( - ) / / n

= (425 -433) / 25 / 42

= −2.074

Test statistic = z = −2.07

P-value = 0.0381

= 0.05  

P-value <

0.0381 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that