Question

please solve only for the set 1.

2. The thrust of a jet engine conditions and a sample of data points was collected. The process was repeated during 3 different data collection sessions. The resulting 3 sets of data are shown in the provided table a) For each data set separately, detemine the sample deviation, S; standard deviation of the mean, SF = s/VN and number of degrees of freedom b) For the data set separately, if one additional measurement were made, estimate the interval in which the value of that measurement measured under the same operating was Set 3 Set 1 Set 2 50.9 52.9 50.1 51.2 48.9 50.3 F; standard 50.3 51.1 51.4 mean. 49.6 51.7 50.5 51.0 49.9 49.7 V. 50.0 48.8 51.6 48.9 52.5 51 would fall (at 95% probability). Provide the interval in the form: FuF. List the corresponding t-value using 3 decimal points c) For each data set separately, determine the true mean (with a 95% probability). Provide your answ d) Compute the pooled mean and standard deviation. Estimate the true mean based on pooled values at the 95% probability. List the t-value using 3 decimal points 50.5 49.5 51.7 50.9 51.3 52.4 49.5 52,4 52.6 er in the form: x1u 51.3 49.4 51.6 50.7 50.3 49.4 52.0 50.3 50.8 49.4 50.2 50.8 49.7 50.9 50.2 KNOWN: Three data sets, N = 20 50.5 52.1 50.1 49.3 50.7 52.3 FIND: a) F, SF, v, and s c) F' Ftrue , b) Ffuture = F t tSf (95%) = F t ts (95%) d) F,Sp, SF, F 49.4 50.7 48.9 mean 49,9 50.5 50.4 49.7 49.2 51.5 SOLUTION

Answer 1

a) At first we will have to find the sample mean and sample standard deviation. We will use the following formulas to find them:

$\\ \overline{F} = \frac1n\sum_{i=1}^n F_i \\ S_F = \frac1n\sum_{i=1}^n F_i^2 - (\overline{F})^2 \\ \nu = n-1 = (19-1) = 18 \ , \ S_{\overline{F}} = S_F/\sqrt{n}$

The below table gives us the output

Sample Size	19
Sample Mean	50.42105263
Sample Standard Deviation	0.9259867837
Standard Deviation of Sample mean	0.2124359375

b) Observe that the t-value corresponding to 0.025 probability for T-distribution of degrees of freedom 18 is 2.101. Hence the interval in which the next observation would be in with 95% probability is

$\\ \overline{F} \pm 2.101S_F = 50.421 \pm 1.945$

c) The true mean will be in the interval with 95% probability is

$\\ \overline{F} \pm 2.101S_{\overline{F}} = 50.421 \pm 0.446$

( The pooled mean and standard deviation can be only calculated for all three sets)