## Chi-square Tests and Hypothesis Testing

The questions below ask about the chi-square test of significance and hypothesis testing. They're hinged on the importance of chi-square tests and ask for hypothesis testing. We have curated only correct answers in each case.

## Chi-Square Test of Significance

One of the reasons Chi-square is one of the most popular types of significance tests used by researchers is because:

Group of answer choices

a) other tests can’t be done using interval-ratio variables

b) it is easy to meet test requirements

c) the sampling distribution, as assumed by the Central Limit Theorem, is normal in shape

**d) all of the above
**

Question 2

Question

A chi-square test compares the ___________ to the __________. If the difference is large, we reject the null hypothesis.

Group of answer choices

**a) expected frequencies; observed frequencies
**

b) independent variables/dependent variables

c) p-value; critical score

Question 3

Question

In a chi-square test, the expected frequencies are:

Group of answer choices

**a) the scores in each cell that would occur if it were due to random chance
**

b) the scores in each cell that were actually observed in the data

c) The sum of the total scores in each row

d) The sum of the total scores in each column

## Hypothesis Testing

Question

When it comes to casino games, the odds of winning at blackjack are better than the odds of winning at roulette or slots. You ask a random sample of Council Bluffs gamblers about their favorite casino game and whether or not they have ever passed a college-level statistics class. The data are summarized in the table below.

Is an understanding of statistics and probability related to favoring games with better odds?

***Conduct a significance test at alpha =.05 and, in step five, calculate the appropriate measures of association if appropriate and write a paragraph summarizing your results.

Favorite Casino Game by Experience in Statistics

Passed a Statistics Class?

Favorite Game Yes No

Blackjack 69 19

Roulette 17 34

Slots 43 75

**Solution
**

- Hypothesis

Null hypothesis: There is no relationship between favorite game and passing a statistic class (they are independent)

Alternative hypothesis: There is a relationship between favorite game and passing a statistic class (they are not independent)

- Level of Significance: α=5%=0.05

Degree of freedom = (r-1)×(c-1)=(3-1)×(2-1)=2

- Critical value = χ^2 (α,df)=5.99

Test statistic

- Test statistic χ^2=∑▒〖(O_i-E_i )^2/E_i =42.7505〗
- Conclusion: Since the test statistic is greater than the critical value, we reject the null hypothesis, which implies that we have enough evidence to support the claim i.e. favorite game and passing a statistic class are not independent i.e. there is a relationship between favorite game and passing a statistic class. Therefore, we conclude that understanding statistics and probability is related to favoring games with better winning odds.