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=50and xbar=140.23lb. Research from other sources suggests that the population of weights of women has a standard deviation given by σ=32.31 lb.

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

b. Find a 99 % confidence interval estimate of the mean weight of all women.

Solutions

Expert Solution

Solution :

Given that,

(a)

Point estimate = sample mean = = 140.23

Population standard deviation = = 32.31

Sample size = n = 50

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576

(b)

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

= 2.576 * (32.31 / 50)

= 11.77

At 99% confidence interval estimate of the population mean is,

- E < < + E

140.23 - 11.77 < < 140.23 + 11.77

128.46 < < 152.00

(128.46 , 152.00)

orchestra answered 2 years ago
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