Zingaro stone printing is a company that specializes in printing images or patterns on polished or unpolished stones. However, for the optimum level of printing of the image the stone surface has to have a Brinell's hardness index of at least 150. Recently, Zingaro has received a batch of polished and unpolished stones from its clients. Use the data provided to answer the following (assuming a 5% significance level); 5.1 Earlier experience of Zingaro with this particular client is favorable as the stone surface was found to be of adequate hardness. However, Zingaro has reason to believe now that the unpolished stones may not be suitable for printing. Do you think Zingaro is justified in thinking so? 5.2 Is the mean hardness of the polished and unpolished stones the same?  Unpolished Treated and Polished 164.4817 133.2094 154.307 138.4828 129.861 159.6652 159.0962 145.6635 135.2567 136.7892 161.8201 167.0866 149.4551 152.6996 135.7143 138.6488 102.0045 163.3844 89.48216 132.1417 95.34903 145.8285 104.4214 162.0816 140.8894 153.7984 147.3666 159.012 48.40684 168.3462 68.25154 132.683 126.1698 151.2739 130.4362 130.9558 120.8943 141.3443 107.2753 171.1147 64.57582 139.7077 136.6501 125.8486 94.63179 152.3545 154.6702 155.1468 75.28981 145.2062 149.0171 168.6528 162.3574 131.9871 113.6495 148.5951 120.4373 138.0538 100.891 134.756 98.86571 142.1568 197.1892 169.3977 158.7379 172.1217 200.1613 159.6643 134.9061 176.6235 170.2872 162.9823 119.3878 133.5345 110.4434 147.8183 166.4437 129.4321 137.2808 129.9385 124.507 123.8134 128.1903 155.3456 160.4276 168.181 58.98137 141.8872 145.179 167.5268 168.3301 150.8986 148.4111 169.3415 165.9483 149.5613 184.5821 192.2729 140.941 141.2311 135.5971 138.9915 181.4705 153.6685 108.524 129.5841 150.3689 143.8767 146.2366 172.591 88.30799 145.5233 141.4386 167.734 192.7358 139.5526 123.5796 152.0563 105.3719 152.0135 187.915 146.2338 135.1917 155.7346 178.0794 154.4155 121.4075 107.5242 157.6923 130.0257 154.8945 153.8186 117.7979 107.5794 126.8547 145.7213 126.474 136.8139 117.01 142.7186 123.0676 142.2935 171.8222 140.1241 88.13599 141.3931 145.1504 131.3705 170.8548 144.5026

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Zingaro stone printing is a company that specializes in printing images or patterns on polished or unpolished stones. However, for the optimum level of printing of the image the stone surface has to have a Brinell's hardness index of at least 150. Recently, Zingaro has received a batch of polished and unpolished stones from its clients. Use the data provided to answer the following (assuming a 5% significance level); 5.1 Earlier experience of Zingaro with this particular client is favorable as the stone surface was found to be of adequate hardness. However, Zingaro has reason to believe now that the unpolished stones may not be suitable for printing. Do you think Zingaro is justified in thinking so? 5.2 Is the mean hardness of the polished and unpolished stones the same? 

Unpolished Treated and Polished
164.4817 133.2094
154.307 138.4828
129.861 159.6652
159.0962 145.6635
135.2567 136.7892
161.8201 167.0866
149.4551 152.6996
135.7143 138.6488
102.0045 163.3844
89.48216 132.1417
95.34903 145.8285
104.4214 162.0816
140.8894 153.7984
147.3666 159.012
48.40684 168.3462
68.25154 132.683
126.1698 151.2739
130.4362 130.9558
120.8943 141.3443
107.2753 171.1147
64.57582 139.7077
136.6501 125.8486
94.63179 152.3545
154.6702 155.1468
75.28981 145.2062
149.0171 168.6528
162.3574 131.9871
113.6495 148.5951
120.4373 138.0538
100.891 134.756
98.86571 142.1568
197.1892 169.3977
158.7379 172.1217
200.1613 159.6643
134.9061 176.6235
170.2872 162.9823
119.3878 133.5345
110.4434 147.8183
166.4437 129.4321
137.2808 129.9385
124.507 123.8134
128.1903 155.3456
160.4276 168.181
58.98137 141.8872
145.179 167.5268
168.3301 150.8986
148.4111 169.3415
165.9483 149.5613
184.5821 192.2729
140.941 141.2311
135.5971 138.9915
181.4705 153.6685
108.524 129.5841
150.3689 143.8767
146.2366 172.591
88.30799 145.5233
141.4386 167.734
192.7358 139.5526
123.5796 152.0563
105.3719 152.0135
187.915 146.2338
135.1917 155.7346
178.0794 154.4155
121.4075 107.5242
157.6923 130.0257
154.8945 153.8186
117.7979 107.5794
126.8547 145.7213
126.474 136.8139
117.01 142.7186
123.0676 142.2935
171.8222 140.1241
88.13599 141.3931
145.1504 131.3705
170.8548 144.5026
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