Question

You have two groups of apples (data below). You want to see if there is a statistical differnce between the two groups. Run descriptives and a two tailed, two sample assuming equal variance t-test.

Here's your data:

Weight of Apples in Grams
Apple ID	Farm A	Farm B
1	131	151
2	147	159
3	134	162
4	134	158
5	136	159
6	137	160
7	140	150
8	134	160
9	136	160
10	133	160
11	134	160
12	132	158
13	139	162
14	136	160
15	135	154
16	135	155
17	135	159
18	138	151
19	134	151
20	149	150
21	149	155
22	135	150
23	148	150
24	135	158
25	149	152
26	137	162
27	134	158
28	140	161
29	138	160
30	133	161
31	140	158
32	138	160
33	150	149
34	135	160
35	136	160
36	148	157
37	150	152
38	136	150
39	142	157
40	132	149
41	133	160
42	147	150
43	135	159
44	140	153
45	132	151
46	132	160
47	136	151
48	141	162
49	136	162
50	135	160
51	142	160
52	135	150
53	132	158
54	140	160
55	136	152
56	138	160
57	132	159
58	136	150
59	136	161
60	135	158
61	135	152
62	136	154
63	137	151
64	138	150
65	137	150
66	136	153
67	134	153
68	139	151
69	133	151
70	136	158
71	149	158
72	140	159
73	135	160
74	135	152
75	131	153
76	137	148
77	139	157
78	132	159
79	138	160
80	139	158
81	148	150
82	136	157
83	133	152
84	135	157
85	149	158
86	139	153
87	137	161
88	136	159
89	135	151
90	138	154
91	134	152
92	140	156
93	135	150
94	141	160
95	142	150
96	138	158
97	132	160
98	136	158
99	141	150
100	135	151

Answer 1

Let $\mu_1,\mu_2$ denote the weight of Apples for Farm A and Farm B respectively.

To test
Hopi = pz
against
217 In: H

Using Excel, (Data -> Data Analysis -> t-Test: Two-Sample Assuming Equal Variances), we get the following output -

File Home Insert Page Layout Formulas Data Review View Help K28 :x , fx B C Farm A Farm B 137.59 155.78 23.31505051 18.29454545 100 100 20.80479798 1 t-Test: Two-Sample Assuming Equal Variances 2 3 4 Mean 5 Variance 6 Observations 7 Pooled Variance 8 Hypothesized Mean Difference 9 df 10 t Stat 11 P(T<=t) one-tail 12 t Critical one-tail 13 P(T<=t) two-tail 14 t Critical two-tail 15 198 -28.19914559 1.45661E-71 1.652585784 2.91323E-71 1.972017478 17

Now,

The value of the test statistic t = -28.199

and critical value = 1.972

Since | test statistic value | > critical value, so we reject H₀ at 5% level of significance and we can conclude that there is significant statistical difference between the two groups.