Question

4. A steel producing company wants to compare between 2 types of blends (A and B) to produce strong steel (based on the weight capacity that can be supported). For this reason, an experiment was carried out to produce steel from each mixture. Observed data are load weights that can be supported, y. The results of the experiment are summarized in the following table:

	Campuran A	Campuran B
Jumlah sampel	11	17
Rata-rata	43.7 ton	48.5 ton
Simpangan baku	24.4 ton	19.9 ton

a. Calculate a 99% confidence interval for the difference from the average weight that can be supported from both mixes! Are you sure, that B mixture can produce stronger steel?
b. So that the interval you make in the problem above is valid, what assumptions are needed?
c. Based on the results in a, are there any real differences regarding the average weights that can be supported from the two mixtures?
d. If it is desired that the difference between the average difference obtained from the sample with the actual average difference is not more than 2 tons with 99% confidence, then how many samples should be taken for each mixture (for this case, each mixture of the same number of samples)?

Answer 1

There are many situations where it is of interest to compare two groups with respect to their mean scores on a continuous outcome. Here we are interested to compare two mixture(Campuran A, Campuran B).

With 99% confidence the difference in mean weight is between -37.079 and 24.079 units. Our best estimate of the difference, the point estimate, is -6 units. The standard error of the difference is 5.32, and the margin of error is 1.26 units. Note that when we generate estimates for a population parameter in a single sample (e.g., the mean [μ]) or population proportion [p]) the resulting confidence interval provides a range of likely values for that parameter. In contrast, when comparing two independent samples in this fashion the confidence interval provides a range of values for the difference. The confidence interval would have been -37.079 to 24.079 suggesting that from 37.079 to 24.079 units lower than Campuran A).

Very small sample size produces a very imprecise estimate of the difference in mean .