Question
In: Math
Using the simple random sample of weights of women from a data set, we obtain these...
Using the simple random sample of weights of women from a data set, we obtain these sample statistics: n equals = 35 and x =146.25 lb. Research from other sources suggests that the population of weights of women has a standard deviation given by sigma σ equals = 30.78 lb. a. Find the best point estimate of the mean weight of all women. b. Find a 95% confidence interval estimate of the mean weight of all women.
Solutions
Expert Solution
Solution :
Given that,
Point estimate = sample mean = 
= 146.25
Population standard deviation = 
= 30.78
Sample size = n =35
At 95% confidence level the z is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
Z/2
= Z0.025 = 1.96
Margin of error = E = Z
/2
* ( 
/
= 1.96 * ( 30.78 /
= 10.1974
At 95% confidence interval estimate of the population mean
is,
- E < 
<
+ E
146.25 - 10.1974 <
< 146.25 + 10.1974
136.0526<
< 156.4474
( 136.0526, 156.4474 )
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