Question

In: Statistics and Probability

From 99 of its restaurants, Noodles & Company managers collected data on per-person sales and the...

From 99 of its restaurants, Noodles & Company managers collected data on per-person sales and the percent of sales due to "potstickers" (a popular food item). Both numerical variables failed tests for normality, so they tried a chi-square test. Each variable was converted into ordinal categories (low, medium, high) using cutoff points that produced roughly equal group sizes. At α = .02, is per-person spending independent of percent of sales from potstickers?

Potsticker % of Sales
  Per Person
Spending
Low Medium High Row Total
  Low 18         7         8         33       
  Medium 10         11         5         26       
  High 12         9         19         40       
  
  Col Total 40         27         32         99       
  
(a)

The hypothesis for the given issue is H0: Percentage of Sales and Per-Person Spending are independent.

  
Yes
No
(b)

Calculate the chi-square test statistic, degrees of freedom, and the p-value. (Round your test statistic value to 2 decimal places and p-value to 4 decimal places. Leave no cells blank - be certain to enter "0" wherever required.)

  
  Test statistic   
  d.f.   
  p-value   
(c) We reject the null and find dependence.
  
Yes
No

Solutions

Expert Solution

Solution:

(a) The hypothesis for the given issue is H0: Percentage of Sales and Per-Person Spending are independent.

Answer: Yes

(b) Calculate the chi-square test statistic, degrees of freedom, and the p-value.

Answer:

Test statistic
df
p-value

(c)

We reject the null and find dependence.

Answer: No

Because the p-value is greater than the significance level 0.02

Explanation:

The observed data is given below:

  Per Person Spending Low Medium High Row Total
  Low 18 7 8 33
  Medium 10 11 5 26
  High 12 9 19 40
  Col Total 40 27 32 99

The expected data is calculated using the below formula:

  Per Person Spending Low Medium High Row Total
  Low 13.33333 9 10.66667 33
  Medium 10.50505 7.090909 8.40404 26
  High 16.16162 10.90909 12.92929 40
  Col Total 40 27 32 99

The chi-square value for each cell is:

  Per Person Spending Low Medium High Row Total
  Low 1.633333 0.444444 0.666667 2.744444
  Medium 0.024281 2.155012 1.3788 3.558093
  High 1.071616 0.334091 2.850387 4.256094
  Col Total 2.729231 2.933547 4.895853



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