Question

An Egg producer wants to estimate the mean number of eggs produced per chicken.  A sample of 16 chickens shows they produced an average of 21 eggs per month with a standard deviation of 1.7 eggs per month.

Develope a 99% confidence interval for the population mean

	a.	[19.27,22.73]
	b.	[20.25,21.75]
	c.	[19.75,22.25]
	d.	[20.09,21.91]

2)

An Egg producer wants to estimate the mean number of eggs produced per chicken.  A sample of 16 chickens shows they produced an average of 21 eggs per month with a standard deviation of 1.7 eggs per month.

What is the best estimate of the population mean?

	a.	1.7
	b.	21
	c.	16
	d.	15

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 21

sample standard deviation = s = 1.7

sample size = n = 16

Degrees of freedom = df = n - 1 = 16 - 1 = 15

1) At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

t/2,df = t0.05,15 =1.753

Margin of error = E = t/2,df * (s /n)

= 1.753* (1.7/ 16)

Margin of error = E = 0.75

The 90% confidence interval is,

- E < < + E

21-0.75 < < 21+0.75

20.25 < < 21.75

b

Point estimate = sample mean = = 21