Question

CANS109   CANS111
270   287
273   216
258   260
204   291
254   210
228   272
282   260
278   294
201   253
264   292
265   280
223   262
274   295
230   230
250   283
275   255
281   295
271   271
263   268
277   225
275   246
278   297
260   302
262   282
273   310
274   305
286   306
236   262
290   222
286   276
278   270
283   280
262   288
277   296
295   281
274   300
272   290
265   284
275   304
263   291
251   277
289   317
242   292
284   215
241   287
276   280
200   311
278   283
283   293
269   285
282   276
267   301
282   285
272   277
277   270
261   275
257   290
278   288
295   287
270   282
268   275
286   279
262   300
272   293
268   290
283   313
256   299
206   300
277   265
252   285
265   294
263   262
281   297
268   272
280   284
289   291
283   306
263   263
273   304
209   288
259   256
287   290
269   284
277   307
234   273
282   283
276   250
272   244
257   231
267   266
204   504
270   284
285   227
273   269
269   282
284   292
276   286
286   281
273   296
289   287
263   285
270   281
279   298
206   289
270   283
270   247
268   279
218   276
251   288
252   284
284   301
278   309
277   284
208   284
271   286
208   303
280   308
269   288
270   303
294   306
292   285
289   289
290   292
215   295
284   283
283   315
279   290
275   247
223   268
220   283
281   305
268   279
272   287
268   285
279   298
217   279
259   274
291   205
291   302
281   296
230   282
276   300
225   284
282   281
276   279
289   255
288   210
268   279
242   286
283   293
277   285
285   288
293   289
248   281
278   297
285   314
292   295
282   257
287   298
277   211
266   275
268   247
273   279
270   303
256   286
297   287
280   287
256   275
262   243
268   274
262   299
293   291
290   281
274   303
292   269

Test the given claim. Identify the null hypothesis, alternative hypothesis, sampling distribution, test statistics, p-value, and conclusion about the null hypothesis. (Assume all requirements are met). 13. Refer to CANS file where CANS109 is the weight of aluminum cans (in grams) before the tops are pressed and CANS111 is the weight of the same aluminum cans (in grams) after the tops are pressed. Use a 0.01 significance level to test the claim that the population mean difference between weight of the aluminum cans before the tops are pressed is the same mean weight after the tops are pressed

Answer 1

Ho :   µd=   0
Ha :   µd ╪   0

t-Test: Paired Two Sample for Means
	CANS109	CANS111
Mean	267.1142857	281.8057143
Variance	488.952381	771.4333005
Observations	175	175
Pearson Correlation	-0.117879788
Hypothesized Mean Difference	0
df	174
t Stat	-5.184621508
P(T<=t) one-tail	2.98035E-07
t Critical one-tail	1.653658017
P(T<=t) two-tail	5.9607E-07
t Critical two-tail	1.97369144

t Stat = -5.18

p value=0.000 <α=0.01, reject Ho

there is enough evidence to reject the claim that

the population mean difference between weight of the aluminum cans before the tops are pressed is the same mean weight after the tops are pressed