Question

You measure 22 dogs' weights, and find they have a mean weight of 35 ounces. Assume the population standard deviation is 13.4 ounces. Based on this, construct a 95% confidence interval for the true population mean dog weight. Give your answers as decimals, to two places

You measure 43 textbooks' weights, and find they have a mean weight of 49 ounces. Assume the population standard deviation is 13 ounces. Based on this, construct a 99% confidence interval for the true population mean textbook weight. Give your answers as decimals, to two places

Answer #1

Solution :

**a)** 95% confidence interval for the true
population mean dog weight

Given that,

= 35

= 13.4

n = 22

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_{/2} = Z_{0.025} =
1.96

Margin of error = E = Z_{/2}* ( /n)

= 1.96 * (13.4 /22)

= 5.60

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

- E < < + E

35 - 5.60 < < 35 + 5.60

29.40 < < 40.60

**(29.40, 40.60)**

**b)** 99% confidence interval for the true
population mean textbook weight.

Given that,

= 49

= 13

n = 43

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_{/2} = Z_{0.005} =
2.576

Margin of error = E = Z_{/2}* ( /n)

= 2.576 * (13 / 43)

= 5.11

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

- E < < + E

49 - 5.11 < < 49 + 5.11

43.89 < < 54.11

**(43.89, 54.11)**

(, )

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