Question

A charity solicits donations by phone. From long experience the charity's director reports that 60 percent of the calls will result in refusal to donate, 30 percent will request more information via the mail, and 10 percent will result in an immediate credit card donation. For a sample of 200 calls last week, 140 refused to donate, 50 requested additional information, and 10 made an immediate donation. At the 0.10 significance level was the sample result different from the usual pattern?

a. State the null and alternate hypothesis

b. State the decision rule.

c. Compute the value of the test statistic.

d. What is your decision regarding the null hypothesis? Interpret the result.

Answer 1

A charity solicits donations by phone. From long experience the charity's director reports that 60 percent of the calls will result in refusal to donate, 30 percent will request more information via the mail, and 10 percent will result in an immediate credit card donation. For a sample of 200 calls last week, 140 refused to donate, 50 requested additional information, and 10 made an immediate donation. At the 0.10 significance level was the sample result different from the usual pattern?

a. State the null and alternate hypothesis

Ho: Donations result same as the usual pattern

H1: Donations result different from the usual pattern

b. State the decision rule.

Critical chi square with 2 df at 0.10 level =4.605

Rejection Rule: Reject Ho if calculated chi square > 4.605

c. Compute the value of the test statistic.

Goodness of Fit Test
	observed	expected	O - E	(O - E)² / E
	140	120.000	20.000	3.333
	50	60.000	-10.000	1.667
	10	20.000	-10.000	5.000
Total	200	200.000	0.000	10.000
	10.000	chi-square
	2	df
	.0067	p-value

d. What is your decision regarding the null hypothesis? Interpret the result.

calculated chi square = 10.000 which is > 4.605. we reject Ho.

We conclude that the donations result different from the usual pattern.