Question

A common breakfast cereal maker states that the sugar content of one of its popular cereal is approximately 36%.

A dataset by W. J. Braun gives the sugar percentages of 100 samples of 25g of the breakfast cereal, collected by using high performance liquid chromatogramphy.

The first 9 values are shown.

36.3, 33.2, 39, 37.3, 40.7, 38.4, 35.8, 36, 37.9…

We will be looking at the mean percentage of the sugar content of the sample in comparison to that of the stated value from the cereal maker.

Answer the following questions.

What is the population? (state and use the correct notation)

What is the sample?(state and use the correct notation)

What is the response variable? Is it categorical or quantitative?

What is the Sample statistic of interest? What’s the value of the sample statistic?(state and use the correct notation)

Answer 1

a) here the population is all breakfast of particular popular cereal that is available in the place where the test is going to conduct.All cereal from all restaurant in the area of study.

b) the sample is the small proportion of population.here the sample is that 100 samples of 25g of breakfast of cereal. ie it is 100 portions each of which are 25g each of cereal

c) here we want to test the sugar level in the cereal, so the response variable is the sugar content of cereal.since it is a numerical value that it can take, so it is a qualitative variable.since whose quality can be measured.

d)We have 100 sample ,from population it is clear that the average sugar content is 36% that means mu = .36

So the sample test Statistic is sample mean,

Since we have 100 sample each denotes the sugar content in cereal.so we want an average value that represents all these value, so we go for the sample mean of these 100, that will provide a better representative value for all these.

It is denoted by xbar.whose value can be only be determined if all 100 values are given.

Which is equal to sum of all xi and then divided by 100

So x bar =(36.3+33.2+39+37.3+........)/100