Question

10. Use the weights of cans of generic soda as sample​ one, and use the weights of cans of the diet version of that soda as sample two. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Construct a 90​% confidence interval estimate of the difference between the mean weight of the cans of generic soda and the mean weight of cans of the diet version of that soda. Does there appear to be a difference between the mean​ weights?

Weight_of_Generic_Soda   Weight_of_Diet_Soda
0.8152   0.8666
0.8494   0.8509
0.8568   0.8327
0.8569   0.8136
0.8621   0.8066
0.8978   0.8167
0.8979   0.8095
0.8896   0.8037
0.8919   0.8197
0.8136   0.8635
0.8165   0.8615
0.8104   0.8633
0.8461   0.8608
0.8273   0.8593
0.8232   0.8664
0.8347   0.8592
0.8494   0.8727
0.8385   0.8552
0.8437   0.8744
0.8441   0.8396
0.8436   0.8165
0.8854   0.8152
0.8705   0.8443
0.8439   0.8372
0.8415   0.8025
0.8517   0.8216
0.8008   0.8096
0.8737   0.8187
0.8253   0.8482
0.8563   0.8404
0.8539   0.8225
0.8533   0.8213
0.8649   0.8238
0.8583   0.8072
0.8589   0.8093
0.8677   0.8177

Assume that population 1 is the generic soda and population 2 is the diet soda.

The 90​% confidence interval is ____ ounces <µ1-µ2<___ ounces.

​(Round to four decimal places as​ needed.)

Does there appear to be a difference between the mean​ weights?

The mean weight for the generic soda appears to be (greater than,less than,equal to) the mean weight for the diet variety because the confidence interval contains (only positive values, zero, only negative values.)

Answer 1

Weight_of_Generic_Soda (X₁ )   Weight_of_Diet_Soda (X₂ )

0.8136 0.8635
0.8165 0.8615
0.8104 0.8633
0.8461 0.8608
0.8152 0.8666
0.8494 0.8509
0.8568 0.8327
0.8569 0.8136
0.8621 0.8066
0.8978 0.8167
0.8979 0.8095
0.8896 0.8037
0.8919 0.8197
0.8273 0.8593
0.8232 0.8664
0.8347 0.8592
0.8494 0.8727
0.8385 0.8552
0.8437 0.8744
0.8441 0.8396
0.8436 0.8165
0.8854 0.8152
0.8705 0.8443
0.8439 0.8372
0.8415 0.8025
0.8517 0.8216
0.8008 0.8096
0.8737 0.8187
0.8253 0.8482
0.8563 0.8404
0.8539 0.8225
0.8533 0.8213
0.8649 0.8238
0.8583 0.8072
0.8589 0.8093
0.8677 0.8177