Students studying statistics are often troubled by hypothesis test and confidence interval homework. Nevertheless, it is an important topic that you must have knowledge about. What hypothesis testing does is provide a basis to take theories and ideas that has been initially developed about economy or markets or investing, and then decide whether the ideas are true or not. To be more precise, hypothesis testing helps in deciding whether tested ideas are probably false or probably true. This is because conclusions made with this process arenâ€™t made with complete confidence.
Estimation and hypothesis testing
In some respects, hypothesis testing is similar to the process of estimation. The field of statistical inference, which involves drawing conclusions on population through observation of subsets of larger group, is usually divided into two groups: hypothesis testing and estimation. As far as estimation is concerned, focus remains on the parameter value, or a range within which the value is likely to fall. On the other hand, focus is shifted with hypothesis testing. Here, a statement is made about the value of the parameter, then the trueness of the statement remains the question.
Hypothesis test explained
For completing your hypothesis test and confidence interval, you should have a clear understanding of what hypothesis testing actually means. As the name would imply, it basically means testing a hypothesis. For instance, if it was believed that the average age of a small townâ€™s inhabitants was 35, then the hypothesis could mean that the average age is still 35 years. For making sure that remains true, suppose a sample of 10 people in the town is taken, and the average age for them is 42. Does this mean that there has been an increase in the mean age of the townâ€™s population? Or is finding mean age of randomly selected sample realistic outcome of the sample? These are the questions hypothesis testing is known to resolve.
Statistics majorly involves probabilities, and same is the case even with hypothesis testing. If it has been decided that the average age of the town is more than 35, one needs to remain open to the possibility of being wrong. That would mean that the mean age is still 35, even though the collected sample suggests otherwise. This means an error, and it would be ideal to minimize the probability of such an error. With a quality hypothesis test and confidence interval homework you can get complete idea of this process.
Two characteristics of sample are vital to its significance in size: mean of the sample and size of the sample. If there is a huge difference between the mean of the sample and original mean, it would be easier to believe intuitively that the mean has increased. On the other hand, if the difference is negligible, it can be believed that the mean hasnâ€™t changed. The second characteristic is size of the sample. The outcome of a larger sample size tends to be more believable that the outcome of a smaller sample size.
Confidence interval is another term you need to be getting used to for your hypothesis test and confidence interval homework. It actually describes the uncertainty about where the mean of the population lies, based on the sample. Confidence interval is calculated using mean. Firstly, the confidence level of the interval is chosen, usually, the level is chosen to be 95%. This shall mean the if the experiment were to be repeated 100 times and corresponding 100 confidence intervals were to be computed, nearly 95 of the confidence intervals would contain the mean of the population.
Need for confidence intervals
- Sample statistics like standard deviation and mean, are mere estimates of the parameters of the population.
- Since the estimates tend to vary from one sample to another, the uncertainty can be quantified with the help of statistically based confidence intervals.
- For population parameters, a range of plausible values is provided by confidence intervals.
- Sample statistics varies from sample to sample, and thus, from the actual population value.
The basic concept of hypothesis test and confidence intervals might be clear to you, but still, there is a lot more to this topic. So, you shouldnâ€™t worry much if you are still having problems with your hypothesis test and confidence interval homework. Instead, you should be looking to get some assistance with your homework. The best way of doing so is hiring online homework help services. These services are aimed at assisting students who are having trouble completing their homework. Not only that, they provide proper guidance through online tutoring to help you have a better grasp of the related subject.
Parametric and Non-Parametric Hypothesis Test
There are two types of hypothesis test:
- With parametric hypothesis, it is assumed that a normal probability distribution is being followed by the data and if there are multiple sets of data, equal variances are used. A test with this hypothesis is basically statement about the parameters of the distribution. (usually the mean)
- On the other hand, with a non-parametric hypothesis, it is assumed that no distribution is being followed by the data. The calculations are usually based on the median.
Steps Involved in hypothesis testing
- The first step is specifying the null and alternative hypothesis. The null hypothesis is denoted by H0, and alternative hypothesis is denoted by H1. Null hypothesis is the claim or statement being made (which is being tried to be disproved), while alternative hypothesis is the hypothesis that needs to be proved or has to be accepted.
- For deciding whether there is significant evidence against null hypothesis for rejecting it in favor of alternative hypothesis, a significance level has to be decided first.
- The next step involves collecting data and deciding whether to reject H0 and accept H1 or accept H0. This can be done either by
- Comparing p-value to significance level, or
- Comparing test statistic to critical value
- The last step involves interpreting the results and drawing a conclusion.
If your homework requires you to test a hypothesis, the above-mentioned steps should definitely help you with your hypothesis test and confidence interval homework.