in the following situation assume the random variable is normally distributed an
ID: 1948502 • Letter: I
Question
in the following situation assume the random variable is normally distributed and use the normal distribution or a t distibution to construct a 90% confidence interval for the population mean.(a) in a random sample of 10 adults from a nearby county. the mean waste generated per person per day was 5.18 pounds and the standard deviation was 1.29 lbs.
(b) repeat part A. assuming the same statistics came from a sampling size of 450. compaire the results.
a. For the sampel of 10 adults the 90% confidence interval is ______ _______
b. question above
Explanation / Answer
a)
= 5.18
= 1.29 / 10 = 0.407933818
Z=(X-)/
For 90 % confidence interval Z = ± 1.65
-1.65 < (X-)/ < 1.65
-1.65 < (X- 5.18 )/ 0.407933818 < 1.65
-0.6730908 < (X- 5.18 )/ 0.6730908
4.507 < X < 5.853
b)
= 5.18
= 1.29 / 450 = 0.060811183
Z=(X-)/
For 90 % confidence interval Z = ± 1.65
-1.65 < (X-)/ < 1.65
-1.65 < (X- 5.18 )/ 0.060811183 < 1.65
-0.100338452 < (X- 5.18 )/ 0.100338452
5.080 < X < 5.280
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