Question

the mean sugar content in breakfast cereal is manufactured to be 11g of sugar per serving- a serving is defined to be 30g of cereal. the manufacturing process is controlled such that the standard deviation is only 0.8 g per serving. after an overhaul of the equipment, the sugar content is checked using a sample of 35 measurements which are averaged to find a mean sugar content of 10.7 g per serving. is there strong evidence that the true mean sugar content has changed due to equipment servicing?

Answer 1

To Test :-
H0 :- µ = 11
H1 :- µ ≠ 11

Test Statistic :-
Z = ( X̅ - µ ) / ( σ / √(n))
Z = ( 10.7 - 11 ) / ( 0.8 / √( 35 ))
Z = -2.2185

Test Criteria :-
Reject null hypothesis if | Z | > Z( α/2 )
Critical value Z(α/2) = Z( 0.05 /2 ) = 1.96
| Z | > Z( α/2 ) = 2.2185 > 1.96
Result :- Reject null hypothesis

Decision based on P value
Reject null hypothesis if P value < α = 0.05 level of significance
P value = 2 * P ( Z > 2.2185 ) = 2 * 1 - P ( Z < 2.2185 ) = 0.0265
Since 0.0265 < 0.05 ,hence we reject null hypothesis
Result :- Reject null hypothesis

There is sufficient evidence to support the claim that  the true mean sugar content has changed due to equipment servicing.