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 )

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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  )

unett · Accepted Answer

Step 1  a) Given,  p^=0.59  n=150  t-table at 95% confidence is  tα2=1.96  Confidence interval =p^±tα2p^(1−p^)n  =0.54±1.960.59(1−0.59)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^(1−p^){n}}  =0.59±1.960.59(1−0.59){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^(1−p^)n  =0.59±1.960.59(1−0.59)1275  =0.59±1.960.00018972549  =0.59±0.0138  =(0.576, 0.604)  Lower bound =0.576  Upper bound =0.604

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

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