UkusakazaL

2021-07-30

A paper reported a $(1-\alpha )$ confidence interval for the proportion of voters is (0.561,0.599) based on a sample of 2,056 people. However, the paper omitted the value of $\alpha$ . If you want to test the hypothesis that the proportion of voters is greater than $65\mathrm{\%}$ at $1\mathrm{\%}$ significance, find $z}_{calc$ value for this problem? Please report your answer to 2 decimal places.

ka1leE

Beginner2021-08-09Added 1 answers

Given data,

Total number of people is 2056.

The proportion of voters is (0.561, 0.599)

Step 1

This is a symmetrical CI.

Hence the sample proportion is expressed as,

Length of CI is expressed as difference between given proportion.

Margin of error is expressed as,

Margin of error(E)

Step 2

Hence the CI of the given proportion with margin of error is,

Hence, the proportions are (0.599,0.561)

The expression for standard deviation is,

Step 3

As know that,

Margin of error

Hence, the value of z is,

Thus

Hence the confidence level is

Step 4

Now, to find null hypothesis:

Here, sample proportion is

Hence the standard deviation at 0.65 claimed proportion,

So the value of

Hence, the value of z is -6.67.