2-2.2. One-Tail Test of the Means in Excel

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Do curso por University of Illinois at Urbana-Champaign

Estatística Inferencial e Preditiva para Negócios

214 classificações

University of Illinois at Urbana-Champaign

Estatística Inferencial e Preditiva para Negócios

214 classificações

Curso 6 de 7 em Specialization Managerial Economics and Business Analysis

Este curso fornece uma estrutura analítica para ajudá-lo a avaliar os principais problemas de uma forma estruturada e irá equipá-lo com ferramentas para melhor gerir as incertezas que permeiam e complicam os processos dos Negócios. O curso tem como objetivo abranger os conceitos estatísticos que se aplicam aos gestores. Vamos considerar dois temas básicos: em primeiro lugar, reconhecendo e descrevendo as variações presentes em tudo que nos cerca, e depois modelando e tomando decisões na presença destas variações. Os conceitos fundamentais estudados neste curso irá reaparecer em muitas outras aulas e ambientes de negócios. Nosso foco será sobre como interpretar o significado dos resultados em um ambiente empresarial e gerencial. Enquanto você será apresentado a parte da ciência do que está sendo ensinado, o foco será em aplicar as metodologias. Isto será realizado através do uso de Excel e usando conjuntos de dados de muitas disciplinas diferentes, permitindo que você veja o uso de estatísticas em cenários muito diversificados. O curso irá focar não só em explicar esses conceitos, mas também a compreensão do significado dos resultados obtidos. Após a conclusão bem sucedida deste curso, você será capaz de: Estabelecer uma opinião sobre uma população. Comparar as diferenças entre populações. Use modelo de regressão linear para a previsão Saber como usar o Excel para análise estatística. Este curso é parte do IMBA oferecido pela Universidade de Illinois, uma forma flexível, totalmente credenciada MBA on-line a um preço extremamente competitivo. Para mais informações, consulte a página Recursos neste curso e onlinemba.illinois.edu.

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Module 2: Statistical Inference Based on Two Samples

Does the medicine a person is taking to treat his condition really work better than a sugar pill? Is the new chip-enabled credit card more secure than the magnetic card? How do you know whether the claims being made about anything being “better than” or “faster than” a competitor are true? In this module we will learn to make this comparison.

2-2.1. One-Tail Test of the Means9:04

2-2.2. One-Tail Test of the Means in Excel5:58

Conheça os instrutores

Fataneh Taghaboni-Dutta
Clinical Professor of Business Administration
University of Illinois, Urbana-Champaign College of Business Department of Business Administration

[SOUND]

The fast food company is considering a new lunch item.

The company will choose the item based on test market results.

The item should show a higher weekly demand than one of the regular

items on the menu.

The analysis needs to show a difference at 0.01 level of significance to be selected.

So we're going to do a hypothesis testing to see whether or not this new item is

indeed has a higher demand than the regular item is benchmarking against.

First thing to do is to write our hypothesis, so

in this case, we will select this new item, if it has an average.

So mu of the new item

is more than mu of the current item that we are benchmarking it against.

Therefore, the null hypothesis should be that it's actually either less or

the same as the current.

Now once I have it written this way I know that we're looking for

mu of the new minus mu of the current is less than or equal to 0, and

the alternate is the other way around, mu minus current is greater than 0.

So now that we know we are doing this, we know that we're doing a one-tail test and

you're right now looking at the differences of being 0, so

let's go to our data.

In our data we see that we have recorded weekly demands, so these are in thousands.

When I say 17, it means that's 17 thousand for that particular time period.

So we have collected data for new item and regular item and

now we can do the analysis.

So go to Data> Data Analysis,

select the t-Test Two-Sample Assuming Unequal Variances.

Variable 1 is in column A, variable 2 is in column B.

Hypothesis difference right now is zero.

I'm going to say that I have labels.

I'm going to change my alpha level to 0.01, and

I'm going to select output range, click here.

Then click here, and press OK.

Okay, so here's our output from our analysis.

And what we are looking for is a one-tail test.

So we have to focus on the one-tail test and that answer is right here.

So we are going to focus our attention in a one-tail test and

these are the information I'm looking at, and specifically on a P,

and we see that our P is less than the alpha of 0.01.

So we'll end up rejecting the null hypothesis.

And what was the null hypothesis?

The null hypothesis was that these two items sell about the same, so

we are rejecting the null,

which means that the new item has a higher demand than the current item.

Now we can go ahead and actually calculate that difference using the equation that we

have the difference between the means,

it's simply the difference between this mean minus this mean.

So on average, there is about 1.31 in thousands higher demand for new

item versus the regular item, but this is just the middle of my confidence interval.

I need to come up with a confidence interval, for that I need my t-value.

Let me explain to you that if I use this t-value,

what I am going to get is actually the 98%.

This t-value is for 0.01, right?

And a 1 tail, which means that I have the entire 0.01.

And if I have .01 here, that means that you are 2.35 standard

errors away from that hypothesis mean difference of 0.

If I use the same T value,

remember, confidence interval is a two-sided value that you get.

You get something plus and minus, the mean.

So there is an .01 also here, and that is negative 2.35.

So if I use this, then I am parking back the 98% confidence interval.

There is .01 on this tail and there is .01 on this tail.

So now you can calculate the standard error.

Standard Error is, when you see the equation you just square root of variance

for the first variable, divided by the sample size for

that and here 75 plus variance for the regular item divided by

the sample size that we have for regular item, and again as you noticed here.

I have different sample sizes, and

as I have mentioned before we're okay with that, we don't need to have same.

So this is the standard error, so now the margin of error is

simply t-value multiplied by standard error.

So this is second term in that equation.

So now we are ready to calculate the lower bound and the upper bound of

the 98% confidence interval, which is the mean difference

minus the margin of error and the mean difference plus the margin of error.

And we can make our life much simpler if I take this value and

multiply it by a thousand.

When I'm talking to people about what we have gotten from our analysis.

What our analysis has shown is that

the new item will sell more than the regular item.

And it can sell by as much as 144,

or as much as 2,480, or anything in between.

So the confidence interval here is quite large.

This seems to be a really,

really good addition, if this was true, whereas this might not be as economical.

Because there is a lot of cost that goes along with introducing a new

item into the menu.

Can be any value in here, and this might be a little too wide for

management to have a useful information when it comes to making a decision,

based on the data that you have.

They may ask you to improve the accuracy and

as you know that comes with increasing the sample size.

So right now management might feel uncomfortable when you show something that

is this wide.

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