Question

5.) The standard IQ test has a mean of 103 and a standard deviation of 1w. We want to be 99% certain that we are within 3 IQ points of the true mean. Determine the required sample size.

16.) When 490 college students were surveyed, 145 said they own their car. Construct a 95% confidence interval for the proportion of college students who say they own their cars.

17.) A survey of 600 non-fatal accidents showed that 279 involved the use of a cell phone. Construct a 99% confidence interval for the proportion of fatal accidents that involved the use of a cell phone.

20.) A researcher at a major hospital wishes to estimate the proportion of the adult population of the United States that has high blood pressure. How large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 2%?

Answer 1

16. n =   490, x =    145
p̄ = x/n = 0.2959

95%   Confidence interval :              

At α = 0.05   , two tailed critical value, z crit = NORM.S.INV(   0.05   / 2) =    1.960

Lower Bound   = p̄ - z-crit*(√( p̄ *(1- p̄ )/n)) =   0.2555          

Upper Bound   = p̄ + z-crit*(√( p̄ *(1- p̄ )/n)) =   0.3363          

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17. n =   600, x =    279
p̄ = x/n = 0.465

99%   Confidence interval :              

At α =    0.01   , two tailed critical value, z crit = NORM.S.INV(   0.01   / 2) =    2.576

Lower Bound   = p̄ - z-crit*(√( p̄ *(1- p̄ )/n)) =   0.4126          

Upper Bound   = p̄ + z-crit*(√( p̄ *(1- p̄ )/n)) =   0.5174          

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20. Let sample proportion, p =    0.5      
Margin of error, E = 2% = 0.02      
Significance level, α = 1-0.99 =  0.01      
Critical value, z = NORM.S.INV( 0.01 /2) =    2.5758

Sample size, n = (z² * p * (1-p)) / E²      
=   4146.8104 = 4147   

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Note: Q5 is not correct. please check it again. with this data sample size is coming as 1.