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Ho : No change in strength due to time Ho : No change in strength due to heat treatment temperature Ho : No change in strength due to interaction of time and heat treatment temperature u uuuuuSolution Use two-way ANOVA to test the above hypothesis. Input the above data as shown below. List1={1,1,1,1,2,2,2,2} List2={1,1,2,2,1,1,2,2} List3={113,116,139,132,133,131,126,122} Define List 3 (the data for each group) as Dependent. Define List 1 and List 2 (the factor numbers for each data item in List 3) as Factor A and Factor B respectively. Executing the test produces the following results. •Time differential (A) level of significance P = 0.2458019517 The level of significance (p = 0.2458019517) is greater than the significance level (0.05), so the hypothesis is not rejected. •Temperature differential (B) level of significance P = 0.04222398836 The level of significance (p = 0.04222398836) is less than the significance level (0.05), so the hypothesis is rejected. •Interaction (A . B) level of significance P = 2.78169946e-3 The level of significance (p = 2.78169946e-3) is less than the significance level (0.05), so the hypothesis is rejected. The above test indicates that the time differential is not significant, the temperature differential is significant, and interaction is highly significant. 20011101 u uuuuuInput Example 1-2-25 Tests (TEST) u uuuuuResults 20010101 Confidence Interval (INTR) 1-3-1 1-3 Confidence Interval (INTR) A confidence interval is a range (interval) that includes a statistical value, usually the population mean. A confidence interval that is too broad makes it difficult to get an idea of where the population value (true value) is located. A narrow confidence interval, on the other hand, limits the population value and makes it difficult to obtain reliable results. The most commonly used confidence levels are 95% and 99%. Raising the confidence level broadens the confidence interval, while lowering the confidence level narrows the confidence level, but it also increases the chance of accidently overlooking the population value. With a 95% confidence interval, for example, the population value is not included within the resulting intervals 5% of the time. When you plan to conduct a survey and then t test and Z test the data, you must also consider the sample size, confidence interval width, and confidence level. The confidence level changes in accordance with the application. 1-Sample Z Interval calculates the confidence interval for an unknown population mean when the population standard deviation is known. 2-Sample Z Interval calculates the confidence interval for the difference between two population means when the population standard deviations of two samples are known. 1-Prop Z Interval calculates the confidence interval for an unknown proportion of successes. 2-Prop Z Interval calculates the confidence interval for the difference between the propotion of successes in two populations. 1-Sample t Interval calculates the confidence interval for an unknown population mean when the population standard deviation is unknown. 2-Sample t Interval calculates the confidence interval for the difference between two population means when both population standard deviations are unknown. On the initial STAT Mode screen, press 4 (INTR) to display the confidence interval menu, which contains the following items. • 4(INTR)b(Z) ... Z intervals (p. 1-3-3) c(T) ... t intervals (p. 1-3-8) # There is no graphing for confidence interval functions. 20011101 Confidence Interval (INTR) 1-3-2 u uuuuuGeneral Confidence Interval Precautions Inputting a value in the range of 0 < C-Level < 1 for the C-Level setting sets you value you input. Inputting a value in the range of 1 < C-Level < 100 sets a value equivalent to your input divided by 100. # Inputting a value of 100 or greater, or a negative value causes an error (Ma ERROR). 20010101 k kkkkkZ Interval 1-3-3 Confidence Interval (INTR) u uuuuu1-Sample Z Interval 1-Sample Z Interval calculates the confidence interval for an unknown population mean when the population standard deviation is known. The following is the confidence interval. Left = o – Z .2 . . 2 n . Right = o + Z n However, .is the level of significance. The value 100 (1 – .) % is the confidence level. When the confidence level is 95%, for example, inputting 0.95 produces 1 – 0.95 = 0.05 = .. Perform the following key operations from the statistical data list. 4(INTR) b(Z) b(1-Smpl) The following shows the meaning of each item in the case of list data specification. Data ............................ data type C-Level ........................ confidence level (0 < C-Level < 1) ................................... population standard deviation (. > 0) List .............................. list whose contents you want to use as sample data (List 1 to 20) Freq ............................. sample frequency (1 or List 1 to 20) Save Res ..................... list for storage of calculation results (None or List...

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