Question

A researcher wants to determine if there is a significant difference in the mean cost of a meal in the world's most expensive restaurants. A survey of 100 people in the most expensive restaurant in the world in Tokyo, Japan produced an average cost per person of $277 and a standard deviation of $35. A survey of 100 people in the second most expensive restaurant located in Toronto, Canada produced an average cost per person of $213 with a standard deviation of $55. Test at the .10 level of significance. What is the value of the test statistic?

Answer 1

Here we want to determine , "wether there is a significant difference in the mean cost of a meal in the world's most expensive restaurants".

So null hypothesis(H₀ ) and alternative hypothesis (Ha ) are as follow:

Null hyypothesis :

Alternative hypothesis :

Where is the population mean of the expenditure restaurant in the world in Tokyo, Japan

and is the population mean of the expenditure restaurant in Toronto, Canada

Here we need to test the difference between the two means so we need to use two sample t test.

If the standard deviations of two populations are assume equal, then we use pooled t test otherwise we use unpooled t test.

So first we need to decide is it pooled t test or unpooled t test by using F test?

Let's use minitab:

Step 1) Click on Stat >>>Basic Statistics >>>2-Variances ...

Fill the necessary information and then click on Option again fill the necessary information.

Look the following image:

Then click on OK again Click on OK , so we get the following output:

p-value = 0.000

Since p-value < 0.10 we reject the equality assumption of two populations.

So that the unpooled procedure more appropriate in this situation

Now lets test the equality of two means using pooled t test:

Level of significance = = 0.10

therfore level of confidence = 100 - 5 = 90%

Let's used minitab:

Steps 1) Click on Stat>>>Basic Statistics>>>2-Sample t...

Steps 1) Click on summarized data and then fill the required information in the boxes : look the following picture.

step 3) Click on Option, Look the following image :

then click on OK again click on OK

So we get the following output

From the above output

Test statistic value =  T-Value = 9.82

p-value = 0.000

Decision rule: 1) If p-value <= level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.000< 0.10 so we used first rule.

That is we reject null hypothesis

Conclusion: At 10% level of significance the data provide evidence that there is a significant difference in the mean cost of a meal in the world's most expensive restaurants.