Question

 

Part I. To build a CI, we need to use a point estimate, a critical value corresponding to a confidence level, and a standard error. Explain how the CI changes (becomes wider or narrower) if we a) increase the sample size or
b) decrease the confidence level

Part II. If constructing a confidence interval for a difference, what number (null value) should the confidence interval not include to conclude a statistically meaningful difference.

Part III. If constructing a confidence interval for a ratio, what number (null value) should the confidence interval not include to conclude a statistically meaningful difference.

Part IV. If we build three hundred 95% confidence intervals based on representative samples, how many confidence intervals do we expect to capture the population parameter? How many do we expect will not capture the population parameter?

Answer 1

Part I. To build a CI, we need to use a point estimate, a critical value corresponding to a confidence level, and a standard
error. Explain how the CI changes (becomes wider or narrower) if we a) increase the sample size or
b) decrease the confidence level

The formula to built a CI :

(point estimate - critical value * standard eror, point estimate + critical value * standard eror)

a) Now, if we increase sample size, keeping the other things same, the standard error decreases, resulting a narrower CI than the previous one.

b) If we decrease the confidence level , keeping the other things same, the critical value decreases ( since the level of significance () increases), resulting a narrower CI than the previous one.

Part II. If constructing a confidence interval for a difference, what number (null value) should the confidence interval not include to conclude a statistically meaningful difference.

Any number other than the hypothesized vaule under the null hypothesis (or you can say the claimed value of the differece for  the research, which is 0 in general cases) should not be included to conclude a statistically meaningful differences.

Part III. If constructing a confidence interval for a ratio, what number (null value) should the confidence interval not include to conclude a statistically meaningful difference.

Any number other than the hypothesized vaule under the null hypothesis (or you can say the claimed value of the ratio for  the research, which is 1 in general cases) should not be included to conclude a statistically meaningful differences.

Part IV. If we build three hundred 95% confidence intervals based on representative samples, how many confidence intervals do we expect to capture the population parameter? How many do we expect will not capture the population parameter?

Confidence Intervals includes the true population parameter 95% of time. That is : 300*(95/100) = 285 confidence intervals we can expect to capture the population parameter.

Confidence Intervals does not include the true population parameter 5% of the time. That is : 300*(5/100) = 15 confidence intervals we can expect , will not capture the population parameter.