Question

1. You’re a beer brewer and you’re interested in whether there is a relationship between the weight of grains used to brew the beer, and the percent alcohol of the beer. You record your data below of your homebrew. (3 points)

Weight of Grains	Alcohol Percentage
9.9	4.3
10.3	4.5
9.8	6.1
9.1	4.5
10.3	5.1
11.1	6.3
10.8	5.8
11.3	4.6
9.9	11.2
10.6	9.2
10.3	4.9
11.4	5.4
11.9	6.3
11.6	5.2
10.8	10
9.4	9.3
10.5	6.5
11	4.9
10.9	8.7
9.6	9.6
10.3	11

1. What kind of statistical test will you be performing?

2. Will you need to test for equal variance? If so, what are your results and how does that influence the next steps in your analysis?

3. What are your null and alternative hypotheses?

H₀:

H_A:

4. Discuss the results of your analysis. Will you accept or reject your null hypothesis? Why? What can you specifically say about the data?

Answer 1

a:

Here we need to find the relationship between two quantitative variables so test for correlation coefficient will be used.

(b)

No, there is no need to conduct test for equal variance.

(c)

(d)

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	9.9	4.3	98.01	18.49	42.57
	10.3	4.5	106.09	20.25	46.35
	9.8	6.1	96.04	37.21	59.78
	9.1	4.5	82.81	20.25	40.95
	10.3	5.1	106.09	26.01	52.53
	11.1	6.3	123.21	39.69	69.93
	10.8	5.8	116.64	33.64	62.64
	11.3	4.6	127.69	21.16	51.98
	9.9	11.2	98.01	125.44	110.88
	10.6	9.2	112.36	84.64	97.52
	10.3	4.9	106.09	24.01	50.47
	11.4	5.4	129.96	29.16	61.56
	11.9	6.3	141.61	39.69	74.97
	11.6	5.2	134.56	27.04	60.32
	10.8	10	116.64	100	108
	9.4	9.3	88.36	86.49	87.42
	10.5	6.5	110.25	42.25	68.25
	11	4.9	121	24.01	53.9
	10.9	8.7	118.81	75.69	94.83
	9.6	9.6	92.16	92.16	92.16
	10.3	11	106.09	121	113.3
Total	220.8	143.4	2332.48	1088.28	1500.31

-------------------------------------------------------

Conclusion: We cannot conclude that there is significant relationship between the variables.  That is we cannot conclude that there is a relationship between the weight of grains used to brew the beer, and the percent alcohol of the beer.