Question

Suppose your designer team has indicated that each unit of product should be between 50 and 95 mm tall. Are 95% of units of manufactured product likely to meet the engineering design specifications? Answer yes or no and explain why or why not in one single sentence.

Heights are below

Product height (mm)
53
93
43
69
42
78
74
90
90
84
48
56
79
60
53
93
91
67
63
53
75
91
91
93
44

Answer 1

No, from the data we can see that there are 4 observations which are outside of the interval 50 to 95 and total observations are 25. So, 21/25 = 0.84 which so far from 0.95 that is the proportion of observations is not close to 95.

Also, we can test this using the test of proportionality considering,

H0 : p = 0.95

H1 : p < 0.95