Question

Observations in sample: 50 autos Miles driven until transmission failure 89346 36289 62559 72989 78146 39722...

Observations in sample: 50 autos

Miles driven until transmission failure

89346
36289
62559
72989
78146
39722
76415
29239
89123
65076
70347
65562
88808
93237
57438
98929
71397
37001
119366
72008
76308
122643
57807
75672
51175
84552
29160
97499
101857
26319
78258
145019
67294
66607
95562
75952
67771
56072
34087
63885
122419
73418
86153
89865
62897
90154
68046
37445
117082
81368
72162.4
26060.92

Question: How many autos should be used in a random sample if we would like the population mean miles driven until transmission failure to be estimated with a margin of error of 3000 miles at the 99% confidence level? (Use the sample standard deviation as the planning value for the population standard deviation.)

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Answer #1

from above data std deviation =26406.64

for 99 % CI value of z= 2.576
standard deviation σ= 26406.64
margin of error E = 3000
required sample size n=(zσ/E)2                                         = 515.0

(try 516 if z value =2.58 taken with 2 decimal places only )

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