For children in the low income group, find a 95% confidence interval for the pro

Question

For children in the low income group, find a 95% 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? Preview Confidence interval supports claim Confidence interval does not support claim For the high income group, find a 99% confidence interval for the mean nickel diameter. e) Critical value (positive value only): f) Margin of error: g) Confidence interval: h) Does the confidence interval support the claim that average nickel size drawn by children from the high income is less than 22 mm? Preview Confidence interval supports claim Confidence interval does not support claim

Explanation / Answer

Alpha = 1-0.95 = 0.0
x = 20,
n = 40 ,
p(hat) = 20/40 = 0.50

a.
critical value = Za/2
= Z0.005
= 1.96

b.
standard error, SE = sqrt(phat(1-phat)/n)
SE = sqrt(0.50(1-0.50) / 40) = 0.07906

margin of error:
= Za/2 * SE
= 1.96* 0.07906
= 0.15495

c.
confidence interval:
phat +/- margin of error
0.5 +/- 0.15495
0.34505 <p< 0.65495

d.
H0: p = 0.40
H1: p > 0.40 (claim)
Since confidence interval include 0.40 .Fail to reject H0.
Confidence interval does not support claim

......................

e) critical value= Zalpha/2=2.576

for rest part additional information needed as we dont know sample mean and sample standard deviation .

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