Question

Suppose that you are testing the hypotheses H0​: p=0.18 vs. HA​: p=/ 0.18. A sample of size 150 results in a sample proportion of 0.25.

​a) Construct a 99​% confidence interval for p. ​

b) Based on the confidence​ interval, can you reject H0 at a =0.01​? Explain.

​c) What is the difference between the standard error and standard deviation of the sample​ proportion?

​d) Which is used in computing the confidence​ interval?

Answer 1

Here we have given that,

The hypothesis is as follows,

v/s

n=number of observation = 150

P=population proportion =0.18

=sample proportion = 0.25

Now we want to find the 99% confidence interval for population proportion P

Formula for CI is as follows,

Now we find Zcritical

=level of significance= 0.01

Zcritical ===2.58

99% confidence interval is

Conclusion:

Here we can say that we are 99 % confident that the population proportion is lies within that interval.

(B)

P=population proportion =0.18

Here 99% CI contain the population proportion value.

we make conclusion to reject or not to reject hypothesis using P-value method here we only conclude that there are 99% confidence that the population proportion 0.18 is falls within this confidence limits.

(C)

we know that

the standard error is the measure of the how far the sample proportion is likely to the from the true population proportion

and standard deviation is the measure of dispersion for the subject form the sample proportion. and here which is used for the 99% confidence interval. both are measure of variation.