A sample selected from a population gave a sample proportion equal to 0.59 .

Sinead Mcgee

Sinead Mcgee

Answered question

2021-09-30

A sample selected from a population gave a sample proportion equal to 0.59 .
Round your answers to three decimal places.
a) Make a 95% confidence interval for p assuming n=150
( Enter your answer; confidence interval assuming n=150, lower bound ,Enter your answer; confidence interval assuming n=150, upper bound )
b) Construct a 95% confidence interval for p assuming n=600. ( Enter your answer; confidence interval assuming n=600, lower bound ,Enter your answer; confidence interval assuming n=600, upper bound )
c) Make a 95% confidence interval for p assuming n=1275. ( Enter your answer; confidence interval assuming n=1275, lower bound ,Enter your answer; confidence interval assuming n=1275, upper bound )

Answer & Explanation

unett

unett

Skilled2021-10-01Added 119 answers

Step 1
a) Given,
p^=0.59
n=150
t-table at 95% confidence is
tα2=1.96
Confidence interval =p^±tα2p^(1p^)n
=0.54±1.960.59(10.59)150
=0.59±1.960.16126666
=0.59±0.0402
=(0.550, 0.630)
Lower Bound=0.550
Upper Bound =0.630
Step 2
b) n=600
p^=0.59
tα2=1.96
CI=p^±tα2p^(1p^){n}}
=0.59±1.960.59(10.59){600}}
=0.59±1.960.00040316666
=0.59±0.0201
=(0.570, 0.610)
Lower Bound =0.570
Upper Bound =0.610
Step 3
c) n=1275
p^=0.59
tα2=1.96
CI=p^±tα2p^(1p^)n
=0.59±1.960.59(10.59)1275
=0.59±1.960.00018972549
=0.59±0.0138
=(0.576, 0.604)
Lower bound =0.576
Upper bound =0.604

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