Question

A college dining hall manager believes that swimmers eat more calories per day than non-swimmers. The dining hall manager wants to assess that claim, so they record the calories that a random sample of 24 college swimmers and a random sample of 24 college non-swimmers eat from the dining hall in the day. We define group 1 to be non-swimmers and group 2 as swimmers.

Which type of procedure should be performed, a confident interval or hypothesis test?

Answer 1

Answer: Hypothesis test.

Explanation:

From our question, we have 2 samples, one from swimmers the other from non swimmers with both having their mean values.

Both data have the same sample size.

The initial sentence is that swimmers eat more calories a day than non swimmers, this sentence is the null hypothesis and it is referring to the difference in the population mean of number of swimmer and non swimmer that eat more calories.

The dinning hall manager has another claim (in opposite direction to the initial claim) that goes against the initial claim.

This is the alternative hypothesis.

Since our sample size is lesser than 30 ( n= 24) and we will be making use of the sample standard deviation, hence a t test will be used as the test statistics.

All of these are the process of performing an hypothesis testing on difference between 2 sample mean assuming u1 ≠ u2

Where u1 = population mean of swimmers who eats calories, u2 = population mean of non swimmers who eat calories.

Answer 2

`\mu_1` represent the mean calores for the group swimmers

`\mu_2` represent the mean calores for the group non swimmers

And for this case we want to tst the following system of hypothesis:

Null Hypothesis:
`\mu_1 \leq \mu_2`

Alternative Hypothesis:
`\mu_1 >\mu_2`

And we can use a t test in order to compare the two means from the two groups of 24

Explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

Solution to the problem

For this case we define the following proportions:

`\mu_1` represent the mean calores for the group swimmers

`\mu_2` represent the mean calores for the group non swimmers

And for this case we want to tst the following system of hypothesis:

Null Hypothesis:
`\mu_1 \leq \mu_2`

Alternative Hypothesis:
`\mu_1 >\mu_2`

And we can use a z test in order to compare the two means from the two groups of 24