Question

Does anybody have something to suggest?

The number of bicycles in each sampled house is noted, from a simple random sample of 400 houses taken in a large city. The avg number of bicycles in the sampled houses is 1.8 and the SD is 1.3. Among the sampled houses, 10% had no bicycle.


An approximate 99% confidence interval for the percent of city houses that have no bicycles goes from X (%) to Y (%).

Find the X and Y.

Thank you!

Answer 1

@amistre64 any suggestions? I found X = 0.127 and Y = 0.2329 but is wrong.

Answer 2

.10 have no bikes; so .90 have bikes

.10 +- zsqrt(.1*.9/400)

sound about right?

or i may be confusing the mean with a proportion ....

Answer 3

@amistre64 I was thinking about it but nothing... I dont understand.. it asks for a 99% confidence interval..

Answer 4

a 99% confidence interval of no bike houses; we want 5% to the left and right of the population proportion of no bikes:

i think the avg and sd given are distractors

\[.10\pm Error_{.05}\]
Error is 2.576sqrt(.1*.9/400) = .03864

but im not all that confident yet that im reading it right

Answer 5

im assuming n, i think we need to determine

Answer 6

let me get back to this ... its almost time to go home

Answer 7

.06136 to .13864 is what i keep ending up with:

thats a 99% CI of 10% of the population having no dogs

Answer 8

@amistre64 i do not agree about the 5%... 5% on the left and 5% on the right is 90%. We want 99% percent which means 0.5% on the left and 0.5% on the right.. Isnt it?

Answer 9

i dont agree with it either .... it was a stray thought while trying to interpret the setup :)

Answer 10

we want a 99% confidence interval for 10% of the sample

Answer 11

I will suicide.. ahahaha

Answer 12

\[\hat p\pm[2.576]\left(\sqrt{\frac{pq}{n}}\right)\]

Answer 13

the zscore associated with a 99% interval is 2.576 ... which is what we use that info for

Answer 14

phat = 10% therefore pq = .1*.9 ; froma sample size of n=400

Answer 15

I cannot think now...really.. I will see it tomorrow on morning. If you think about it just tell me...Thank you again..

Answer 16

@amistre64 0.061 to 0.139 i tried it is wrong..

Answer 17

@amistre64 you know what I was thinking about? because it says for the city houses with no bikes. Maybe we have to take this as a seperate population with n=40.

Answer 18

so for n= 40 we get: -0.22 to 0,222

Just an idea.

Answer 19

X=1.6934 and Y=1.9064.