In a four-digit lottery, each of the four digits is supposed to have the same probability of...

Question:

In a four-digit lottery, each of the four digits is supposed to have the same probability of occurrence. The table shows the frequency of occurrence of each digit for 68 consecutive daily four-digit drawings

Digit Frequency
0 19
1 30
2 26
3 26
4 45
5 35
6 17
7 18
8 20
9 36
Total 272

a. The hypothesis for the given issue is {eq}H_0: {/eq} The digits come from a uniform population.

A. No.

B. Yes.

b. Calculate the Chi-square test statistic, degrees of freedom and the p-value.

c. Find the citical value of the Chi-square for {eq}\alpha = .01 {/eq}

d. At {eq}\alpha = .01 {/eq} , can you reject the hypothesis that the digits are from a uniform populatiion?

Pearson's chi-squared test ({eq}\chi^2 {/eq}):

It tests a null hypothesis stating that the frequency distribution of certain events observed in a sample is consistent with a particular theoretical distribution.

Answer and Explanation: 1

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a) The hypothesis for this problem will be

{eq}H_0:\text{Digits come from a uniform distribution} \: vs \:H_1:\text{Digits does not come from a...

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The Chi-Square Test

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Chapter 2 / Lesson 13
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What if you expect one thing, but get another? The chi-square test is a method of statistical analysis that can help us identify if the results from a genetic cross are simply due to chance, or if something else is happening. Learn about the chi-square test in this lesson.


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