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A generic engineering company claims that it has developed a genetically modified tomato plant that yields on average more tomatoes than other varieties. A farmer wants to test the claim on a small scale before committing to a full-scale planting. Ten genetically modified tomato plants are grown from seeds along with ten other tomato plants. At the season's end, the resulting yields in pound are recorded as below.

Sample 1 (genetically modified): 20, 23, 27, 25, 25, 25, 27, 23, 24, 22 Sample 2 (regular): 21, 21, 22, 18, 20, 20, 18, 25, 23, 20

a. Construct the 99% confidence interval for the difference in the population means based on these data.

b. Test, at the 1% level of significance, whether the data provide sufficient evidence to conclude that the mean yield of the genetically modified variety is greater than that for the standard variety.

For a on my calculator I went to STAT- EDIT- Input data into L1 & L2 then found the difference in L3. Then back to STAT- CALC- 1- Var Stats. That did not work. How would I solve a?

For b I did alpha= .01/2= .005 and looked on my T-Chart to get this answer: 2.576 After this step I am not sure what to do.

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  • $\begingroup$ We cannot tell you how to answer this question on your calculator--we don't even know what its capabilities are. You ought to contemplate how you would perform these procedures using only basic arithmetic and Student t tables. $\endgroup$ – whuber Nov 28 '16 at 18:41
  • $\begingroup$ It's a TI-84 Plus Silver Edition. I wouldn't be asking this question if I didn't know how to do it by hand or using a calculator. This isnt basic arithmetic either. Thank you. $\endgroup$ – Kimberly Nov 28 '16 at 21:17
  • $\begingroup$ 2.576 is the critical value for the t distirbution. If the observed value of your t statistic is larger than 2.576 you can reject the null hypothesis. $\endgroup$ – Michael R. Chernick Nov 28 '16 at 22:59

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