Example 1 of parameter hypothesis test under 0-1 Population Distribution

[Case] recruitment and testing problems the human resources department of a company wants to recruit several engineers in a certain professional field. There are 10 multiple-choice questions, and each question has four alternative answers. Only one of them is correct. Or, the correct ratio is only 0.25. How many correct answers should be given before admission can be considered?

(1) If I have five questions, do I have to consider admission?

(2) If I have 6 questions, do I have to consider admission?

I. Qualitative Analysis:

1. Overall distribution of B (1, p)

If you are correct, the value of X is 1 (equivalent to an uneven coin with the front facing up). If you are wrong, the value of X is 0.

B (1, p) Distribution Properties: E (X) = p, D (X) = p (1-p ).

2. For a completely guessed candidate, the probability of a correct answer is 0.25, that is, p = 0.25.

3. For any candidate, we do not know whether or not he guessed it (not sure what his p value is). Let's assume that:

(H0): p = 0.25, alternative hypothesis (H1): p> 0.25

4. This is obviously a single-side test problem.

Ii. Quantitative Analysis

Determine the statistic of the test

The applicant answers 10 questions, which is equivalent to 10 samples: X1, X2 ,......, X10

We cannot use statistics for testing, because we do not know the distribution form (we only know its mean and variance)

However, we fully understand the statistic Y = x1 + x2 + ...... + The distribution of x10, that is, the binary distribution B (10, p), and the value of the statistic Y can be calculated. Therefore, we can use Y for hypothesis testing.

Note that Y is the number of correct answers (because xi = 0 when an error is returned)

So can we export the contradiction between the distribution of Y and the number of actually correct questions?

The following table lists the probability formulas of two distributions:

From this we can see that when r = 6, the sum of all probabilities not less than r is 0.0197 <a = 0.05

Iii. Inspection

Set k to the observed value of Y. If k = 5, it should be:

 

In this case, no conflicts are exported and the original assumptions cannot be rejected. There is no significant difference between the student and the guess, and admission is not considered.

If k = 6, there are:

In this case, the export conflicts and the original assumptions are rejected. The student is significantly different from the guess. You can consider admission.

New questions:

A company needs to recruit engineers and issue 100 "Incorrect" multiple-choice questions. Q: How many answers can be considered for admission?

Next article:Example 1 of parameter hypothesis test in the 0-1 Population Distribution (implemented by SPSS)