1. Marine scientists are studying great white sharks. Here are lengths in feet o
ID: 3127634 • Letter: 1
Question
1. Marine scientists are studying great white sharks. Here are lengths in feet of an SRS of 20 great whites measured: 17.6 12.4 17.9 16.6 14.8 18.7 16.4 15.9 18.3 14.6 15.2 14.3 15.7 16.1 13.7 19.3 16.2 17.3 13.2 15.5
(a) Make a stem plot of these data.
(b) Does it seem safe to use the t procedures to analyze these data? Explain.
(c) Regardless of your answer above, given x-bar = 15.99 and s = 1.85 find a 95% confidence interval for the mean length of great whites
(d) Interpret the interval above.
Explanation / Answer
a.
b.
Yes it is
c.
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=15.99
Standard deviation( sd )=1.85
Sample Size(n)=20
Confidence Interval = [ 15.99 ± t a/2 ( 1.85/ Sqrt ( 20) ) ]
= [ 15.99 - 2.093 * (0.414) , 15.99 + 2.093 * (0.414) ]
= [ 15.124,16.856 ]
d.
Interpretations:
1) We are 95% sure that the interval [ 15.124,16.856 ] contains the true population
mean
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contain the true
population mean
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