Question

A government official is in charge of allocating social programs throughout the city of Vancouver. He will decide where these social outreach programs should be located based on the percentage of residents living below the poverty line in each region of the city. He takes a simple random sample of 127 people living in Gastown and finds that 22 have an annual income that is below the poverty line.

Use the sample data to compute a 95% confidence interval for the true proportion of Gastown residents living below the poverty line.

(Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places).

95% confidence interval = ( , )

Answer #1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 22 / 127 = 0.173228

1 - = 1 - 0.173228 =0.826772

Z/2 = Z0.025 = 1.96

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 * (((0.173228 * 0.826772) /127 )

= 0.065820

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.173228 - 0.065820 < p < 0.173228 + 0.065820

0.107 < p < 0.239

**95% confidence interval =( 0.107 ,0.239 )**

A government official is in charge of allocating social programs
throughout the city of Vancouver. He will decide where these social
outreach programs should be located based on the percentage of
residents living below the poverty line in each region of the city.
He takes a simple random sample of 127 people living in Gastown and
finds that 21 have an annual income that is below the poverty
line.
Part i) The proportion of the 127 people who are living...

A government official is in charge of allocating social programs
throughout the city of Vancouver. He will decide where these social
outreach programs should be located based on the percentage of
residents living below the poverty line in each region of the city.
He takes a simple random sample of 129 people living in Gastown and
finds that 20 have an annual income that is below the poverty
line.
Use the sample data to compute a 95% confidence interval for...

A government official is in charge of allocating social programs
throughout the city of Vancouver. He will decide where these social
outreach programs should be located based on the percentage of
residents living below the poverty line in each region of the city.
He takes a simple random sample of 129 people living in Gastown and
finds that 25 have an annual income that is below the poverty
line.
Use the sample data to compute a 95% confidence interval for...

A government official is in charge of allocating social programs
throughout the city of Vancouver. He will decide where these social
outreach programs should be located based on the percentage of
residents living below the poverty line in each region of the city.
He takes a simple random sample of 125 people living in Gastown and
finds that 20 have an annual income that is below the poverty
line.
Part i) The proportion of the 125 people who are living...

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