Question

1-What is the significance of central limit theorem?
2. Give an example where confidence interval must be used for statistical inference.
3. Give an example where hypothesis testing must be used for statistical inference.
4. What is P-value?
5. What is the relationship between hypothesis test and confidence interval?

Answer 1

1. The significance of central limit theorem is that irrespective of the distribution of the population if the sample size is high enough then the distribution of the sample means will be normal.

2. If we want to measure the proportion of people who are left-handed then confidence interval must be used to estimate this proportion because it depends on many factors and varies on the basis of these factors.

3. If we want to check whether the male’s height is less than 5.5 in New York then hypothesis testing must be used for this purpose.

4. The P-value is the probability of observing the sample assuming that the null hypothesis is true.

5. The hypothesis test is carried out to infer about the population characteristic using a point estimate and confidence interval is also calculated to infer about the population characteristic using interval estimate but while calculating these interval estimates we make use of point estimates hence both of these are related to each other in terms of using point estimates.

There is one more way to define the relationship between the two:

When constructing of 95% confidence interval, all values in the interval are considered plausible for the parameter being estimated. The values outside this interval are rejected as relatively implausible. If the value of the parameter specified by the null hypotheses is contained in the 95% interval, then the null hypothesis cannot be rejected at the level of 0.05 levels. If the value specified by the null hypothesis is not in the interval, then the null hypothesis can be rejected at the 0.05 level. If a 99% confidence interval is constructed, the values outside the interval are rejected at the 0.01 level.