Question

Question 6 1 pts A quality control lab has just purchased a new analytical instrument to replace the old one that has served for more than 10 years. Daily operation of the old instrument include running a sample of the same batch for 10 years as quality assurance measure. The old method yielded over all these years an average value of 10.5 ppm with a standard deviation of 0.2 ppm. The new instrument has been tested for a week and the first results are shown below 10.0 ppm 10.4 ppm 10.2 ppm 10.8 ppm 10.1 ppm 10.5 ppm 10.1 ppm Compare the old and new instrument, can you assume at 99% confidence level that the new instrument gives a different result than the old instrument? Perform a significance test and select the correct answer O texp 1.89 o 3.707 exp? tcnt, therefore reject null hypothesis. results can be considered different at 99% confidence interval. exp 1.89, tom 3.707 texpC tent, therefore retain null hypothesis. results cannot be considered different at 99% confidence interval O texp 2.04 to 3.707 expS tent, therefore retain null hypothesis: results cannot be considered different at 99% confidence interval texp 1.89; tet 3.499 texpC tent, therefore retain null hypothesis: results cannot be considered different at 99% confidence interval

Answer 1

The following data is given: S. No. (in Results ppm) 10.0 10.4 10.2 10.8 10.1 10.5 10.1 Determine the mean and standard deviation as shown below: Mean (T)- D 10.0+10.4+10.2-10.8+10.1-10.5-10.1 =103 Z(D-) Standard deviation (0) n-1 10.0-(10.3)] +(10.4 -(10.3)) +(10.2 - 10.3)) +(10.8- (10.3) V-10.1-(10.3)) +(10.5-10-3)) + (10.1-(10.3)) 6-1 = 0.28 Calculate the value of texeriment as shown below: tealculated = 1 1103-10.51 028/ =1.89 Hence, the value of taxperimen is 1.89

Determine the degree of freedom as shown below: Degree of freedom = 7-1 = 7-1 =6 This value is determined by examining the standard t-table. The value corresponding to 6 degrees of freedom at 99% was found out to be 3.707428 from the standard t-value table. Thus, the value of ticaat 99 % confidence interval is 3.07 in 3 sig figs). The tra is greater than the typerime, the null hypothesis is retained but the confidence level is rejected. The correct option is D The t imest al, therefore retain null hypothesis, results cannot be considered different at 99 % confidence interval.