Question

What is the impact of widening the margin of error?

Question 9 options:

	The confidence level increases.
	The confidence level decreases.
	The confidence level stays the same.
	It is unclear what the confidence level does. You dropped out of DePaul to pursue your passion as an amateur entomologist. Congrats,...I guess. You collect 25 cockroaches and measure the width of their thorax. The mean is 1.7 cm and you know the standard deviation of the population's thorax width is 0.25. Calculate the 95% confidence interval. Question 10 options: 1.7 +/- 1.96 1.7 +/- 0.02 1.7 +/- 0.10 1.7 +/- 1.65 What if you had collected 50 cockroaches instead? Question 11 options: 1.7 +/- 0.07 1.7 +/- 0.001 1.7 +/- 0.01 1.7 +/- .02 What if you had collected 100 cockroaches instead? Question 12 options: 1.7 +/- 0.02 1.7 +/- 0.005 1.7 +/- 0.05 1.7 +/- .002

Answer 1

Solution :

9)

Confidence level increases .

Given that,

= 1.7

= 0.25

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

(a)

n = 25

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

= 1.96 * (0.25 / 25)

= 0.10

At 95% confidence interval estimate of the population mean is,

E

1.7 0.10

(b)

n = 50

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

= 1.96 * (0.25 / 50)

= 0.07

At 95% confidence interval estimate of the population mean is,

E

1.7 0.07

(c)

n = 100

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

= 1.96 * (0.25 / 100)

= 0.05

At 95% confidence interval estimate of the population mean is,

E

1.7 0.05