10.7 Tests Concerning Differences Between Means for Small Samples Advanced Math Topics 10.7 Tests Concerning Differences Between Means for Small Samples

Hint: In this lesson, just like yesterday’s, we are comparing two sample means. The difference is that in today’s lesson, the sample means come from small samples (n < 30). Thus, we have different formulas and need the t-chart (not the z-chart) in the back of the book.

A chemist at a paint factory claims to have developed a new paint that will dry quickly. The manufacturer compares this new paint with its fastest drying paint. He tests 5 cans of each and finds that the current paint has an average drying time of 45.4 minutes with a standard deviation of 1.949 minutes. The new paint has an average drying time of 43.4 minutes with a standard deviation of 1.14 minutes. Using a 5% level of significance, test the claim of the chemist. Steps Steps 1) Use the formula… 1) = 1.597 Round however you wish, the more the merrier! 2) Use the formula and the result from step 1… 2) = 1.98 3) Figure if it’s a 1-tail or 2-tail test and look up the appropriate column in the t-table in the back of the book with df = n1 + n2 – 2 3) It is a 1-tail test so look up t0.05 with df = 8 t = 1.86 4) Compare your answers from steps 2 and 3 to see if you can conclude that there is a significant difference between the two means. 4) Since our sample t-value of 1.98 is outside the t-value from the chart, the answer is… “There is a significant difference. The paint does dry quicker!”

From the HW P. 510 An engineer is testing the number of defective items produced by the day shift and the night shift of an assembly line. The engineer tested 15 day shifts and found the average number of defective items to be 21.3 with a standard deviation of 2.61. He tested 13 night shifts and found the average to be 25.6 with a standard deviation of 3.04. At a 5% level of significance, does the data indicate a difference in the mean number of defective items produced by both shifts? t = -4.03 which is outside the acceptance region of t = -2.056 to t = 2.056. There is a significant difference in the means.

P. 510 #1-5 I will be out Friday at a conference. Test Monday. HW P. 510 #1-5 I will be out Friday at a conference. Test Monday.