Construct a 99% confidence interval of the population proportion at the given level of confidence. x=240, n=300 the lower bound is? the upper bound is?

lower bound = 0.7404; upper bound = 0.8596

Step-by-step explanation:

The proportion p for this population:

p =

p = 0.8

Confidence interval for proportion is calculated as:

p ± z-score.

Z-score for a 99% confidence interval is: z = 2.58

Calculating:

0.8 ± 2.58.

0.8 ± 2.58.

0.8 ± 2.58(0.0231)

0.8 ± 0.0596

This means that the lower limit of this interval is 0.7404 and upper bound is 0.8596

n

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for