Question

For children in the low income group, find a 90% confidence interval for the proportion of children that drew the nickel too large.

Give all answers correct to 3 decimal places.

a) Critical value (positive value only):

b) Margin of error:

c) Confidence interval:

d) Does the confidence interval support the claim that more than 40% of children from the low income group draw nickels too large?

• Confidence interval supports claim
• Confidence interval does not support claim

Data shown below

The correct size of a nickel is 21.21 millimeters. Based on that, the data can be summarized into the following table:

	Too Small	Too Large	Total
Low Income	18	22	40
High Income	19	16	35
Total	37	38	75

Based on this data: (give your answers as fractions, or decimals to at least 3 decimal places)

a) The proportion of children from the low income group that drew the nickel too large is: .55Correct  

b) The proportion of children from the high income group that drew the nickel too large is: .457Correct  

c) The proportion of all children that drew the nickel too large is: .507Correct  

d) If a child is picked at random, what is the probability they are in the low income group, given they drew the nickel too large? .579Correct  

Keep your answers handy; you will need them again later.

For the high income group, find a 98% confidence interval for the mean nickel diameter.

e) Critical value (positive value only):

f) Margin of error:

g) Confidence interval: < μμ <

h) Does the confidence interval support the claim that average nickel size drawn by children from the high income is less than 22 mm?

• Confidence interval supports claim
• Confidence interval does not support claim

Data shown below

High Income
	22
	19
	22
	18
	24
	18
	18
	23
	23
	23
	16
	16
	22
	11
	27
	25
	29
	17
	20
	23
	17
	25
	14
	15
	21
	26
	20
	25
	18
	26
	21
	18
	15
	23
	11

Answer 1

Part 1:

d) Since the lower limit>0.40 so we are 95% confident that the confidence interval supports the claim that more than 40% of children from the low income group draw nickels too large.

Part 2:

a) The proportion of children from the low income group that drew the nickel too large is:22/40=  0.55

b) The proportion of children from the high income group that drew the nickel too large is: 16/35=0.457.

c) The proportion of all children that drew the nickel too large is:38/75=0.507.

d) If a child is picked at random, the probability they are in the low income group, given they drew the nickel too large=22/38=0.579.

Keep your answers handy; you will need them again later.

For the high income group, find a 98% confidence interval for the mean nickel diameter.

e)

f)

g)

h) Since 22 lies in the CI so the confidence interval does not support the claim that average nickel size drawn by children from the high income is less than 22 mm.