The critical value for a chi-squared test with df = 4 and α = 0.01 to test the uniform distribution of customer preferences among five coffee brands is 14.860.
Step-by-step explanation:
The student is asking for the critical value (x0) to test the claim that the distribution of customer preferences among five different brands of coffee is uniform. Given the sample size of 200 customers and the level of significance α = 0.01, we need to find the appropriate critical value from the chi-squared distribution table with degrees of freedom df = 5 - 1 = 4. Since the sample size is large enough, the chi-squared distribution is appropriate for this hypothesis test.
To determine the critical value, we look up the chi-squared table for df = 4 and α = 0.01. The corresponding critical value is option B: 14.860.
The probable question can be:
A coffeehouse wishes to see if customers have any preference among 5 different brands of coffee. A sample of 200 customers provided the data below. Find the critical value x Xo to test the claim that the distribution is uniform. Use a = 0.01.
Brand
1
2
3
4
5
Customers
55
30
32
65
18
A. 9.488
B. 14.860
C. 13.277
D. 11.143