Question

In: Statistics and Probability

A researcher wishes to estimate the proportion of adults who have high-speed internet access. What size...

A researcher wishes to estimate the proportion of adults who have high-speed internet access. What size sample should be obtained if she wishes the estimate to be within 0.01 with 90% confidence if...

a. She uses a previous estimate of 0.42? N=

b. She does not use any prior estimates? N=

Solutions

Expert Solution

Solution :

Given that,

= 0.42

1 - = 1 - 0.42= 0.58

margin of error = E = 0.01

At 90% confidence level z

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table ( see the 0.05 value in standard normal (z) table corresponding z value is 1.645 )   

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.645 / 0.01)2 * 0.42 * 0.58

=6592

Sample size = 6592

(b)

Solution :

Given that,

= 0.5 ( assume 0.5)

1 - = 1 - 0.5= 0.5

margin of error = E = 0.01

At 90% confidence level z

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table ( see the 0.05 value in standard normal (z) table corresponding z value is 1.645 )   

Sample size = n = (Z/2 / E)2 * * (1 - )

= (1.645 / 0.01)2 * 0.5 * 0.5

=6765

Sample size = 6765


Related Solutions

A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size...
A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.03 with 95 % confidence if (a) she uses a previous estimate of 0.34 ? (b) she does not use any prior estimates?
A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size...
A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.01 with 90& confidence if ​(a) she uses a previous estimate of 0.42 ​(b) she does not use any prior​ estimates?
A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size...
A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.04 with 99​% confidence if ​(a) she uses a previous estimate of 0.34​? ​(b) she does not use any prior​ estimates?
A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size...
A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.05 with 99​% confidence if ​a) she uses a previous estimate of 0.54​? ​b) she does not use any prior​ estimates?
A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size...
A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.02 with 90​% confidence if ​a) she uses a previous estimate of 0.28​? ​ b) she does not use any prior​ estimates? ​ a) nequals nothing ​(Round up to the nearest​ integer.) ​b) nequals nothing ​(Round up to the nearest​ integer.)
A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size...
A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.05 with 99% confidence if (a) she uses a previous estimate of 0.54? (b)she does not use any prior estimates?
A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size...
A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.04 with 99% confidence if ​(a) she uses a previous estimate of 0.28​? (b) she does not use any prior​ estimates?
A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size...
A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.01 with 95% confidence if: ​(a) she uses a previous estimate of .42? ​(b) she does not use any prior​ estimates?
A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size...
A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.04 with 95 % confidence: a) assuming a previous study concluded that the proportion of adults who have high-speed internet access was 0.48? b) assuming the researcher has no previous results to reference?
A researcher wishes to estimate the proportion of adults who have high-speed internet access. What size...
A researcher wishes to estimate the proportion of adults who have high-speed internet access. What size sample should be obtained if she wishes the estimate to be within 0.04 with 99% confidence if a) she uses a previous estimate of 0.36? b) she does not use any prior estimates?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT