Question

F	G
0	76.15
1	75.63
2	74.67
3	73.69
4	72.71
5	71.72
6	70.73
7	69.74
8	68.75
9	67.76
10	66.76
11	65.77
12	64.78
13	63.79
14	62.8
15	61.82
16	60.84
17	59.88
18	58.91
19	57.96
20	57.01
21	56.08
22	55.14
23	54.22
24	53.29
25	52.37
26	51.44
27	50.52
28	49.59
29	48.67
30	47.75
31	46.82
32	45.9
33	44.98
34	44.06
35	43.14
36	42.22
37	41.3
38	40.38
39	39.46
40	38.54
41	37.63
42	36.72
43	35.81
44	34.9
45	34
46	33.11
47	32.22
48	31.34
49	30.46
50	29.6
51	28.75
52	27.9
53	27.07
54	26.25
55	25.43
56	24.63
57	23.83
58	23.05
59	22.27
60	21.51
61	20.75
62	20
63	19.27
64	18.53
65	17.81
66	17.09
67	16.38
68	15.68
69	14.98
70	14.3
71	13.63
72	12.97
73	12.33
74	11.7
75	11.08
76	10.48
77	9.89
78	9.33
79	8.77
80	8.24
81	7.72
82	7.23
83	6.75
84	6.3
85	5.87
86	5.45
87	5.06
88	4.69
89	4.35
90	4.03
91	3.73
92	3.46
93	3.21
94	2.99
95	2.8
96	2.63
97	2.48
98	2.34
99	2.22
100	2.11

1. Use columns F and G for the Least-Squares line.

1. Use Excel to make a scatter plot of the dat
2. Adjust the values of the x and y axes so that the data is centered in the plot.
3. Put the trendline on your plot.
4. Put the equation of the trendline on your plot.
5. Put the R² value on your plot.
6. The R value is a measure of how well the data fits a line. What is R? Is R + or - ?
7. Make a screen shot of your final plot. How well do you think the data fits the line? (good fit, moderate fit, marginal fit, no fit)

2. A brand of mints come in various flavors. The company says that it makes the mints in the following proportions.

Flavor	Cherry	Strawberry	Chocolate	Orange	Lime
Expected %	30%	20%	20%	15%	15%

A bag bought at random has the following number of mints in it.

Flavor	Cherry	Strawberry	Chocolate	Orange	Lime
Observed	67	50	54	29	25

Determine whether this distribution is consistent with company’s stated proportions.

1. What is the null hypothesis?
2. What is the alternative hypothesis?
3. Enter the observed number of times a flavor comes up in your test bag and the expected number of times that the flavor should come up into the X-squared goodness of fit applet.
4. What is the number of degrees of freedom?
5. What is the p-value? Provide a screen shot of your answer.
6. Using a 95% confidence interval, should you accept or reject the null hypothesis?
7. Does the distribution of flavors in your random bag support or contest the company’s state proportions? (yes or no).

3. This problem is the check to see whether you understand the X-squared test. There are only 2 test columns, so you cannot use the X-squared Goodness of Fit applet from the previous problem as it requires 3 or more test intervals.

You are told that a genetics theory says the ratio of tall:short plants is 3:1. You test this claim by growing 200 plants. You obtain 160 tall plants and 40 short plants. Using a X-squared test, determine whether or not your results supports the tall:short = 3:1 claim.

1. What is the null hypothesis for this test?
2. What is the alternative hypothesis?
3. Fill in the following table.

Card Color	Observed	Expected	(O – E)	(O-E)2	(O-E)2/E
Red	160
Black	40
Sum	200	200	0	n/a

4. What is the value of X² for this data?
5. What is the number of degrees of freedom?
6. Use the X² calculator to compute p (use the right tail option). Provide a screen shot of your calculation.
7. Does this value of p support the null hypothesis at the 10% significance level? (yes or no and explain using your numbers)

Answer 1

a) First the data is enterd in 2 columns of excel -> Select the data -> Insert -> Scatter plot-> the plot appears as follows:

select the points on the plot -> Layout -> Trendline -> More trendline options -> Select "Linear" in Trend Type -> Close -> The trend line appears as follows:

select the points on the plot -> Layout -> Trendline -> More trendline options -> Enable "Display Equation on chart" -> Close -> The equation appears as follows:

Here G = y, F = x in the equation.

select the points on the plot -> Layout -> Trendline -> More trendline options -> Enable "Display R squared value on chart" -> Close -> The R square value appears as follows:

f) R2= 0.983

R = - 0.991 , -ve since as F increases G decreases and slope of the line is also negative.

g) Since 98.3% of the variability in G is explained by the linear regression due to G on F so It is a very good fit.