Out of a sample 650 high school students, 321 take the bus to school every day. construct a 99% confidence interval for the popu

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Out of a sample 650 high school students, 321 take the bus to school every day. construct a 99% confidence interval for the popu

lation mean of high school students that take the bus to school every day.
a.ci=(43.23%,51.18%)
b.ci=(44.34%, 54.43%)
c.ci=(45.54%, 53.23%)
d.ci=(46.16%,52.16%)

Mathematics

1 answer:

gtnhenbr [62] · Answer 1 · 2023-05-07T18:54:43+03:00

A 99% confidence interval for the population mean of high school students that take the bus to school every day is b) ci=(44.34%, 54.43%)

We need to find the 99% confidence interval for the population mean of high school students that take the bus to school everyday

A confidence interval is a range of estimates for an unknown parameter. The confidence interval is calculated at the specified confidence level; the most common is the 95% confidence level, but sometimes other levels are used, such as 90% or 99%.

The confidence interval of proportions is given by:

π ± z √(π (1-π) /n)

π is the sample proportion.

z is the critical value.

n is the sample size.

For 99% confidence interval the value of z is 2.58

π = 321/650

The confidence interval is given by

=321/650 ± 2.58 √( (321/650) × [ 1 - (321/650) ] ÷ 650)

= (0.493846 ± 0.050594)

=(0.4434 , 0.5443)

=(44.34 % , 54.43 %)