Question

1.You want to investigate the potential for a new organic bread product, and will conduct a research study involving the preferences of consumers. Suppose that, in the judgment of management, the product should not be introduced unless at least the average household would spend at least $6.90 per month on this bread, and that the research calls for 31 respondents to be interviewed for their preferences.

1. State the null and alternate hypotheses.
2. The attached database shows the amount spent on bread for each of the 31 households. What is the average amount spent per household? What is the standard error?
3. Can you reject your null hypothesis? (For a t-test, using 0.05 significance level and a sample size of 31, the correct tabled t-value is 2.042). State clearly, in plain English, your conclusion regarding the null hypothesis. Include an Excel printout or screen shot to show how you arrived at your conclusion.

Family	Spend
1	8.04
2	6.22
3	7.21
4	8.76
5	10.24
6	6.41
7	7.02
8	7.52
9	6.87
10	7.89
11	8.31
12	6.89
13	7.01
14	7.89
15	8.1
16	8.32
17	8.66
18	12.12
19	7.54
20	9.88
21	10.76
22	5.21
23	9.89
24	11.84
25	8.89
26	11.32
27	8.55
28	4.65
29	9.09
30	9.87
31	8.91

Answer 1

(a)

Ho: ≥ 6.90

Ha: < 6.90

Null hypothesis states that the average household spent on bread per month is at least $6.90 i.e. 6.90 or greater.

Alternative hypothesis states that the average household spent on bread per month is less than $6.90

(b)

sample mean = sum of all terms / no of terms = 259.880 / 31 = 8.3832

Standard error = std dev / sqrt(n)

Std dev= s

data	data-mean	(data - mean)2
8.04	-0.3432	0.11778624
6.22	-2.1632	4.67943424
7.21	-1.1732	1.37639824
8.76	0.3768	0.14197824
10.24	1.8568	3.44770624
6.41	-1.9732	3.89351824
7.02	-1.3632	1.85831424
7.52	-0.8632	0.74511424
6.87	-1.5132	2.28977424
7.89	-0.4932	0.24324624
8.31	-0.0732	0.00535824
6.89	-1.4932	2.22964624
7.01	-1.3732	1.88567824
7.89	-0.4932	0.24324624
8.1	-0.2832	0.08020224
8.32	-0.0632	0.00399424
8.66	0.2768	0.07661824
12.12	3.7368	13.96367424
7.54	-0.8432	0.71098624
9.88	1.4968	2.24041024
10.76	2.3768	5.64917824
5.21	-3.1732	10.06919824
9.89	1.5068	2.27044624
11.84	3.4568	11.94946624
8.89	0.5068	0.25684624
11.32	2.9368	8.62479424
8.55	0.1668	0.02782224
4.65	-3.7332	13.93678224
9.09	0.7068	0.49956624
9.87	1.4868	2.21057424
8.91	0.5268	0.27751824

t = 4.6163

As the t stat falls in the rejection area, we reject the Null hypothesis.

Hence we have sufficient evidence to believe that the average household spent on bread per month is less than $6.90