Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 445 gram setting. It is believed that the machine is underfilling the bags. A 34 bag sample had a mean of 443 grams. Assume the population standard deviation is known to be 30. 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 :

= 445

=443

=30

n = 34

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 445

Ha :     445

Test statistic = z

= ( - ) / / n

= (443-445) /30 / 34

= 0.39

Test statistic = z = 0.39

P(z > 0.39 ) = 1 - P(z < 0.39 ) = 1 -0.6517

P-value =2 * 0.3483 =0.7766

= 0.05  

P-value >

0.7766 > 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that