Question

The Tinned Fruit Company introduced a new range of mid-sized tins of fruit earlier this year. The company claims that the mean weight of these tins of fruit are on average 200g, with a standard deviation of 12g. Recently however, a consumer organisation has received a number of complaints from consumers who believe that the mean weight of their tins containing nectarines is actually less than 200g. To investigate this discrepancy, the consumer organisation randomly selects 1500 tins of nectarines produced in July and records the weight of these tins. This sample is then used to assess whether the company is marketing tins of nectarines that weigh on average less than 200g

1) what is the null and alternative hypothesis?

2) do we reject or accept the null hypothesis

Answer 1

1) null hypothesis H0:200

alternate hypothesis Ha:<200

her we want to assess whether the company is marketing tins of nectarines that weigh on average less than 200g, so the alternate hypothesis will be :<200 and opposite of alternate hypothesis the null hypothesis is 200

(2) here we use Z-test and statistic z=(-)/()=(-)/sqrt(n))=(-200)/(12/sqrt(1500))=(-200)/0.3098

the typical critical left one-tailed  Z(0.05)=-1.645

if the observed statistic z=(-200)/0.3098 will be less than -1.645, then we reject null hypothesis and conclude that the company is marketing tins of nectarines that weigh on average less than 200g other-wise we accept H0.

so value is needed for this part , please share it.

Here only first part of the question can be answered as the sample mean of 1500 tins (of nectarines produced in July and records the weight of these tins is not given )

If you need any assistance/help please respond back at earliest