Question

In: Statistics and Probability

Suppose a certain species bird has an average weight of x=3.85 grams. Based on previous studies,...

Suppose a certain species bird has an average weight of x=3.85 grams. Based on previous studies, we can assume that the weights of these birds have a normal distribution with 0=0.29 grams. For a small group of 17 birds, find a 75% confidence interval for the average weights of these birds.

Expert Solution

Solution :

Given that,

$\bar x$ = 3.85

= 0.29

n = 17

At 75% confidence level the z is ,

$\alpha$ = 1 - 75% = 1 - 0.75 = 0.25

$\alpha$ / 2 = 0.25 / 2 = 0.125

Z_/2 = Z_0.255 = 1.15

Margin of error = E = Z_/2* ( / $\sqrt$ n)

= 1.15* (0.29 / $\sqrt$ 17)

= 0.08

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

$\bar x$ - E < $\mu$ < $\bar x$ + E

3.85-0.08 < $\mu$ < 3.85+0.08

3.77< $\mu$ < 3.93

orchestra answered 2 years ago

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