Question

A survey of 548 citizens found that 363 of them favor a new bill introduced by the city. we want to find a 95% confidence interval for the true proportion of the population who favor the bill.
what is the lower limit of the interval? ( Round to 3 decimal digits)

Answer 1

We are given 363 citizens to favor the new bill out of 548.

The formula for the confidence interval for the true proportion of the population is:

where,

is the sample proportion,

n is the sample size.

Let us first find the critical value of Z at 95%

So,

Thus,

Now, we have to look up at the Z standard normal table for an area of 0.9750.

So, we get:

Now,

Now, we have got all the findings, we just need to put the values in the formula:

Thus, the upper bound =

Lower bound =

*NOTE:- The result may be slightly differ due to decimal roundings.

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