Question

A makeup company wants to know if all the shades of their foundation are sold at equal rates. Below is the gathered data.

Shade #1	Shade #2	Shade #3	Shade #4	Shade #5	Shade #6	Shade #7
218	191	239	189	178	168	149
Pearson's Chi-square test
X-squared = 28.88	df = 6	p_value = ?

Based on the information above, determine if you should accept or reject the null hypothesis that there is no relationship between shade number and number of units sold when alpha = 0.05?

Answer 1

Test statistic, X-squared = 28.88

Degrees of freedom = 7 - 1 = 6

P-value = 0.000064

Since, the P-value is less than the significance level of 0.05, we should reject the null hypothesis that there is no relationship between shade number and number of units sold.

Edit:

P-value for Chi-square distribution can be calculated from Chi-square distribution table. But from table you can calculate the p-value (by linear interpolation) if the p-value can be bounded within 0.001 and 0.05. You cannot calculate it if the p-value is less than 0.001 (in this case p-value is 0.000064). In this case, you have to use a statistical calculator or a statistical software (eg R-Studio, Python etc) or some online calculator. Here is a link of an online p-value calculator:

https://www.danielsoper.com/statcalc/calculator.aspx?id=11