Question

1 uestion Help The following contingency table breaks down a month of customer complaints received by a retailer. Some of those complaining are long-term customers, whereas the rest are recent. There are four types of complaints. Complete parts (a) and (b) below. Type of Complaint Sales Billing Store Lack of Person Display Inventory Customer Long-term 25 28 26 Status Recent Error 113 OC. Ho: Customer status and type of complaint have equal proportions H: Customer status and type of complaint have non-equal proportions UD. Ho: Customer status and type of complaint are dependent H: Customer status and type of complaint are independent 30 Compute the chi-squared test statistic. x2 = (Round to three decimal places as needed.)

Answer 1

	Sales person	Billing error	Store Display	Lack of Inventory
Long Term	64	25	28	26	143
Recent	113	27	42	10	192
	177	52	70	36	335

We now calculate the proportion of each complaint type belonging to the two categories.

	Sales person	Billing error	Store Display	Lack of Inventory
Long Term	64/335 * 143 = 27.32	25/335 * 143 = 10.67	28/335 * 143 = 11.95	26/335 * 143 = 11.09	143
Recent	113/335 * 192 = 64.76	27/335* 192 = 15.47	42/335 * 192 = 24.07	10/335 * 192 = 5.73	192
	177	52	70	36	335

Now, the formula for chi-square statistic is
$\chi$ ² = $\sum$ (observed - expected)² / expected
= (64-27.32)²/27.32 + (25-10.67)²/10.67 + (28-11.95)²/11.95 + (26-11.09)²/11.09 + (113-64.76)²/64.76 + (27-15.47)²/15.47 + (42-24.07)²/24.07 + (10-5.73)²/ 5.73
= 49.246 + 19.245 + 21.556 + 20.045 + 35.934 + 8.593 + 13.356 + 3.182
= 171.157