An analyst wonders if the age distribution of customers coming for service in town is the same as at the mall branch. He selects 100 transactions at random from each branch and researches the age information for the associated customer. These are the data :
Age
< 30 30 - 55 56 + Totals
Distribution In town 24 37 35 96
mall 29 49 19 97
Totals 53 86 54 193
Enter your answers or calculations in the yellow cells.
1 Write the null hypothesis regarding distribution of ages by bank locations town and mall branch.
Which type of test is required (goodness of fit, independence, homogeneity)?
2 Compute
Age Groups
< 30 30 - 55 56 +
Expected (E) In town
mall
Age Groups
< 30 30 - 55 56 +
(O - E)2/E In town
mall
3 What is the chi square test statistic? Note: =CHISQ.TEST does not compute the chi-squared test statistic. It computes p-value.
4 What is the degrees of freedom of the chi-squared test statistic?
Use an Excel function to compute the critical value at alpha = 0.05.
5 State your decision about H0 with the significance level. Are the bank distributions the same (Yes/No)?
Analyzing Age Distribution of Customers at Town and Mall Branches
Introduction
In this study, we aim to investigate whether the age distribution of customers seeking services at a town branch is similar to that of a mall branch. By conducting a statistical analysis, we can determine if there are any significant differences in the age groups of customers visiting these two locations.
Thesis Statement
The null hypothesis states that there is no significant difference in the age distribution of customers between the town branch and the mall branch. To test this hypothesis, we will perform a chi-squared test to determine the level of association between age groups and branch locations.
Hypothesis Testing
1. Null Hypothesis (H0): The age distribution of customers at the town branch is the same as that of the mall branch.
2. Type of Test: We will be conducting a goodness-of-fit test to compare the observed and expected frequencies of age groups at each branch location.
Data Analysis
Computation
- We will calculate the expected frequencies for each age group at the town and mall branches based on the total number of transactions.
- Next, we will compute the chi-squared statistic using the formula: ((O - E)^2 / E), where (O) is the observed frequency and (E) is the expected frequency.
Results
3. Chi-Squared Test Statistic: The chi-squared test statistic will provide us with a measure of how well the observed data fit the expected distribution.
4. Degrees of Freedom: The degrees of freedom for the chi-squared test statistic can be calculated based on the number of categories and observations in our data.
5. Decision on H0: Using a significance level of 0.05, we will compare the calculated chi-squared value with the critical value from the chi-squared distribution. Based on this comparison, we will either reject or fail to reject the null hypothesis.
Conclusion
By conducting a thorough analysis of the age distribution of customers at the town and mall branches, we can gain valuable insights into potential differences in customer demographics between these two locations. The results of this study will help businesses tailor their services to better meet the needs of their target customer segments.