Week 7
Week 7: Quantitative analysis 2
Hello all, today I am asked to reflect about the Inferential statistics. as the previous posted the way I need to learn always starting with the definition and how to used, so let's explore it together!!
I'm trying to understand and distinguish between descriptive and inferential statistics in my own way. If you have some discussion, please do not hesitate to discuss more closely about this topic.
The annual income of the Amy clothing company (Million pound)
According to the table, descriptive statistics can be used to tell us about the value of the number in the table. For example, the most sale is in the summer each year. But inferential statistics is about using the statistics for predicting population or situation which will occur in the future. To illustrate in this case, we can estimate in 2019 about the amount of sale by using the statistics to predict trends via statistic theorem. The characteristics of the statistics can be divided into two ways.
How do I know which one of hypothesis that is be chosen?
Null hypothesis should be used when a hypothesis test concerning a population mean, u, should always specify a single value for that parameter. By this it means the null hypothesis should always be of the form
1. Two- tailed test: if we are concerned primarily with deciding whether a population mean is different from null hypothesis, so the equation is that population should not be a not equal sign in the alternative hypothesis. we express an equation as
Terms and Errors
In this section, we need to know 4 keywords including
Test statistic: the statistic use as the basis for deciding whether the null hypothesis should be rejected
Rejection region: the set of values for the test statistic that leads to rejection of null hypothesis.
Non- rejection region: the set of values for the test statistic that leads to non- rejection of null hypothesis.
Critical value: the value of the test statistic that separate the rejection and non- rejection regions.
Type I and Type II Errors
When we employed the statistic inference methods, it is possible that the decision reached incorrect. this because of obtaining partial information from the sample.
There are four outcomes are possible occurred in testing hypothesis as presented in the table below
Type I Error: rejecting the null hypothesis when it is in fact true.
Type II Error: not rejecting the null hypothesis when it is in fact false.
Probability of Type I and Type II Errors the probability of making a type 1 error is called the significance level of the hypothesis test. we used the alpha (α) to symbolize the significance level. in other word, the significance level also means the probability of rejecting a true null hypothesis.
In conclusion for a hypothesis test
Hello all, today I am asked to reflect about the Inferential statistics. as the previous posted the way I need to learn always starting with the definition and how to used, so let's explore it together!!
I'm trying to understand and distinguish between descriptive and inferential statistics in my own way. If you have some discussion, please do not hesitate to discuss more closely about this topic.
The annual income of the Amy clothing company (Million pound)
Year
|
Winter
|
Spring
|
Summer
|
2015
|
6.2
|
7.5
|
10.0
|
2016
|
6.3
|
7.6
|
10.2
|
2017
|
6.2
|
7.6
|
9.8
|
2018
|
6.4
|
7.7
|
11.0
|
According to the table, descriptive statistics can be used to tell us about the value of the number in the table. For example, the most sale is in the summer each year. But inferential statistics is about using the statistics for predicting population or situation which will occur in the future. To illustrate in this case, we can estimate in 2019 about the amount of sale by using the statistics to predict trends via statistic theorem. The characteristics of the statistics can be divided into two ways.
1. Parameter Estimation is the characteristic value of a population. The method of estimating this parameter can be divided into two ways namely point estimation and interval estimation.
2. Hypothesis Test is on of the common use methods for making such decision. A hypothesis is simply a statement that something is true.
Typically, a hypothesis test involves two hypotheses. the first is called "null hypothesis", and the other called "alternative hypothesis" or "research hypothesis"
Typically, a hypothesis test involves two hypotheses. the first is called "null hypothesis", and the other called "alternative hypothesis" or "research hypothesis"
How do I know which one of hypothesis that is be chosen?
Null hypothesis should be used when a hypothesis test concerning a population mean, u, should always specify a single value for that parameter. By this it means the null hypothesis should always be of the form
Alternative hypothesis: the choice of the alternative hypothesis depends on and should reflect the purpose of performing the hypothesis test. Three choices of this type of hypothesis test are
1. Two- tailed test: if we are concerned primarily with deciding whether a population mean is different from null hypothesis, so the equation is that population should not be a not equal sign in the alternative hypothesis. we express an equation as
2. Left- tailed test: if we are concerned primarily with deciding whether a population mean is less than a specified value, then the alternative hypothesis should be as the equation below
3. Right - tailed test: in contrast the left- tail test, if we are concerned primarily with deciding whether a population mean is greater than a specified value, then the alternative hypothesis can be expressed as
In this section, we need to know 4 keywords including
Test statistic: the statistic use as the basis for deciding whether the null hypothesis should be rejected
Rejection region: the set of values for the test statistic that leads to rejection of null hypothesis.
Non- rejection region: the set of values for the test statistic that leads to non- rejection of null hypothesis.
Critical value: the value of the test statistic that separate the rejection and non- rejection regions.
Type I and Type II Errors
When we employed the statistic inference methods, it is possible that the decision reached incorrect. this because of obtaining partial information from the sample.
There are four outcomes are possible occurred in testing hypothesis as presented in the table below
Type I Error: rejecting the null hypothesis when it is in fact true.
Type II Error: not rejecting the null hypothesis when it is in fact false.
Probability of Type I and Type II Errors the probability of making a type 1 error is called the significance level of the hypothesis test. we used the alpha (α) to symbolize the significance level. in other word, the significance level also means the probability of rejecting a true null hypothesis.
In conclusion for a hypothesis test
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