Chapter 10, Problem 72CP

Pick the method Steve Solomon, the owner of Leonardo’s Italian restaurant, wonders whether a redesigned menu will increase, on the average, the amount that customers spend in the restaurant. For the following scenarios, pick a statistical method from this chapter that would be appropriate for analyzing the data, indicating whether the samples are independent or dependent, which parameter is relevant, and what inference method you would use:

1. a. Solomon records the mean sales the week before the change and the week after the change and then wonders whether the difference is “statistically significant.”
2. b. Solomon randomly samples 100 people and shows them each both menus, asking them to give a rating between 0 and 10 for each menu.
3. c. Solomon randomly samples 100 people and shows them each both menus, asking them to give an overall rating of positive or negative to each menu.
4. d. Solomon randomly samples 100 people and randomly separates them into two groups of 50 each. He asks those in Group 1 to give a rating to the old menu and those in Group 2 to give a rating to the new menu, using a 0 to 10 rating scale.

To determine

Pick a statistical method that is appropriate for analyzing the data.

Indicate whether samples are independent or dependent.

Indicate the relevant parameter.

Find the inference method that can be used.

Explanation of Solution

It is given that Person S records the mean sales before and after the change and wanted to check whether the difference is statistically significant.

Statistical method:

This is a significance test as Solomon wanted to check whether the difference is “statistically significant”.

Independent or dependent:

The observations of mean sales in the week before the change are independent with the mean sales in the week after the change. Therefore, the samples are independent.

Relevant parameter:

In order to test whether the difference is significant based on mean sales, the relevant parameter is the mean difference between mean sales.

Inference method:

This scenario refers to the significance test for comparing population means. Thus, the appropriate test can perform using t-statistic and P-value. The null hypothesis is rejected, if P-value is less than or equal to significance level.

To determine

Choose a statistical method that is appropriate for analyzing the data.

Explain whether samples are independent or dependent.

Find the relevant parameter.

Obtain the inference method that can be used.

Explanation of Solution

It is given that Person S randomly samples 100 people and shows them both menus. For each menu, sample is asked to rate between 0 and 10.

Statistical method:

The statistical method is either confidence interval method or significance test.

Independent or dependent:

Since the both menus were showed to same 100 people (that is, two samples involving same subjects), the samples are dependent.

Relevant parameter:

The relevant parameter is the mean difference score of 100 people between two scores of menus.

Inference method:

If statistical method of confidence interval satisfies, then confidence interval calculation would be the inference method for this scenario. Otherwise, t-statistic and P-value method of significance test for comparing population means would be the inference method.

To determine

Select a statistical method that is appropriate for analyzing the data.

Choose whether samples are independent or dependent.

Explain about the relevant parameter.

Prefer the inference method that can be used.

Explanation of Solution

It is given that Person S randomly samples 100 people and shows them both menus. The sample is asked for overall rating (positive or negative) to each menu.

Statistical method:

Overall rating of positive or negative refers to the comparison of proportions. Thus, the method for comparing proportions for dependent sample is either McNemar test of significance or confidence interval (if the confidence interval contains 0).

Independent or dependent:

Since the both menus were showed to same 100 people (that is, two samples involving same subjects), the samples are dependent.

Relevant parameter:

The relevant parameter is the difference between proportions between two scores of menus.

Inference method:

If statistical method of confidence interval satisfies, then confidence interval calculation would be the inference method for this scenario. Otherwise, to compare two proportions

with dependent data, z-score and P-value method using McNemar test would be the inference method.

To determine

State a statistical method that is appropriate for analyzing the data.

Check whether samples are independent or dependent.

Find the relevant parameter.

Obtain the inference method that can be used.

Explanation of Solution

It is given that Person S randomly samples 100 people and randomly separates them into two groups of 50 each. Then, using a 0 to 10 rating scale, group 1 was asked to rate the old menu and group 2 was asked to rate new menu.

Statistical method:

The statistical method is either confidence interval method or significance test.

Independent or dependent:

Since the observations in group 1 and group 2 are not same, (that is, two samples involving different subjects), the samples are independent.

Relevant parameter:

The relevant parameter is the mean difference score between group 1 and group 2.

Inference method:

If statistical method of confidence interval satisfies, then confidence interval calculation would be the inference method for this scenario. Otherwise, t-statistic and P-value method for significance test for comparing population means would be the inference method.