Question

In: Statistics and Probability

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=50 and x overbar=142.71 lb. Research from other sources suggests that the population of weights of women has a standard deviation given by sigma=31.7631.76 lb.

a. Find the best point estimate of the mean weight of all women.

b. Find a 90​% confidence interval estimate of the mean weight of all women.

Solutions

Expert Solution

Solution :

Given that,

= 142.71

= 31.76

n = 50

(a) best point estimate of the mean = 142.71

(b)At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z0.05 = 1.645

Margin of error = E = Z/2* ( /n)

= 1.645 * (31.76 / 50)

= 7.3886

At 90% confidence interval estimate of the population mean is,

- E < < + E

142.71 -7.3886 < < 142.71 +7.3886

135.3214< < 150.0986

(135.3214 , 150.0986)

orchestra answered 2 years ago
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