Question

it is necessary to guarantee that the minimum resistance of a plastic container in a vertical position is 20 kg. To evaluate this, the following data have been obtained through destructive tests. 28.3 26.8 26.6 26.6 28.5 28.1 24.8 27.4 26.2 29.4 28.6 24.9 25.2 30.2 27.2 27.0 26.1 28.1 26.9 28.0 27.6 25.6 29.5 27.2 27.3 26.2 27.7 27.2 25.9 26.5 28.3 26.5 29.1 23.7 29.7 26.8 29.5 28.4 26.3 28.1 28.7 27.0 25.5 26.9 27.2 27.6 25.5 28.3 27.4 28.8 25.0 25.3 27.7 25.2 28.6 27.9 28.7 A) This variable must necessarily be evaluated by sampling and not 100%, why? B) Do an exploratory analysis of this data (get a histogram and see the behavior of the data obtained). C) Estimate, with a confidence of 95%, what is the average resistance of the containers? D) Before the study, it was assumed that μ = 25. Given the evidence in the data, is this assumption correct? E) With the previous data estimate, with a confidence of 95%, what is the population standard deviation (of the process)?

Answer 1

(B) Histogram of the data :

after plotting the histogram, we clearly see that data are normally distributed. that is a bell-shaped curve.

(C) 95 % confidence interval for the average resistance of the container:

95 % confidence interval:
(26.87493, 27.62683)

(D) Before the study, it was assumed that μ = 25. Given the evidence in the data, This assumption is not correct because μ = 25 is not lies within the confidence interval  (26.87493, 27.62683).

(E) The population standard deviation of the process is 1.416878.