Question

The weight of a bushel of standard quality wheat is 60 lbs. But it is claimed that a newly created wheat variety is more dense and hence its mean weight is greater than 60 lbs. per bushel. To test this claim, the weight of bushels from 36 randomly selected fields planted with this new wheat variety were taken

64.2	61.8	62.3	62.9	62.3	60.3
59.8	59.4	59.5	60.5	59.7	60.4
63.2	61.1	63.2	59.7	60.3	59.3
60.8	61.4	58.1	60.2	58.4	58.2
62	60.4	59.4	58.5	56.1	63.2
59.3	60.4	58.2	61.3	63.1	62.1

Give the null and alternative hypotheses for this situation in mathematical notation.

Determine the sample's test statistic.

State a final conclusion regarding the results of the hypothesis test. Make sure your statement is tied to the context of the problem (weight per bushel of this wheat variety).

Answer 1

Here claim is that a newly created wheat variety is more dense and hence its mean weight is greater than 60 lbs.

So hypothesis is vs

For the given data using excel we find mean and standard deviation as below

And

As n=36>30, as per central limit theorem sample mean is normally distributed.

So we will use z distribution

Test statistics is

P value is

Here value of alpha is not given so let us assume it to be 0.05

As P value is less than alpha we reject the null hypothesis

So We have sufficient evidence that for newly created wheat variety is more dense and hence its mean weight is greater than 60 lbs. per bushel.