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

Sample size, n= 35

Sample mean, = 10.7

Population standard deviation, = 0.8

Let be the true mean sugar content.

Null hypothesis, H0 : = 11g

Alternate hypothesis, Ha : 11g

Test statistics = = = -2.2185

Critical region , Z (0.05/2) = 1.96 ; since there is noo significance level mention so we will take 0.05 as default

Since the test statistic lie in the critical region i.e, (-infinity, - 1.96) U ( 1.96 , infinity). So we will reject the null hypothesis.

Hence at 0.05 significance level we have enough evidence that the sugar content has changed due to the equipment serving.