Question

Slot Machines. In the article "The Influence of Theme as Slot Machine Attribute on Casino Gamers Decision-Making" (American Journal of Applied Sciences, Vol. 10, No. 7, pp. 734-739) E. Wannenburg et al. explore the effects of theme on slot-machin gamers. Independent random samples of male and female slot gamer were asked whether the theme of a slot machine plays a role in their slot-machine game selection. The responses are summarized in the following table.

At the1%significance level, do the data provide sufficient evidence to conclude that there is a difference between male and female slot gamers with regard to the way they perceive theme as a slot machine
gamers with regard to the way they perceive theme as a slot machine attribute?

Short answer

P-value is $\left(=0.004\right)<\alpha (=0.01)$
The null hypothesis is rejected at 1% level.
The results are statistically significant at 1% level of significance.

The data provide sufficient evidence to conclude that there is a difference between male and female slot garners with regard to the way they perceive theme as a slot machine attribute at the 1% significance level.

Step-by-step solution

Step 1. Given information

Independent random samples of male and female slot gamer were asked whether the theme of a slot machine plays a role in their slot-machine game selection. The responses are summarized in the following table.

Step 2. Check whether or not the data provide sufficient evidence to conclude that there is a difference between male and female slot garners with regard to the way they perceive theme as a slot machine attribute at 1% significance level. 

Step 1:
The test hypotheses are given below:
Null hypothesis:
H₀ : There is no association exists between gender and response.
Alternative hypothesis:
H₁ : There is an association exists between gender and response.

Decide the level of significance.

Here, the level of significance is,$\alpha =0.01$

Step 4. Find the expected frequency and test statistic. 

MINITAB procedure:
Step 1: Choose Stat > Tables > Chi-Square Test (Two-Way Table in Worksheet).
Step 2: In Columns containing the table, enter the columns of Male and Female.
Step 3: Click OK.

Step 5. Finding the MINITAB output

chi-square test: male,female

From the MINITAB output,the value of the chi-square statistic is $10.821$

Step 6. Finding the value of p and check the above problem by using rejection and interpretation

From the MINITAB output, the P-value is, $0.0004$

Rejection rule:
If P-value$\le \alpha ,$ then reject the null hypothesis.
Here, theP-value is lesser than the level of significance.
That is, P-value$(=0.004)<\alpha (=0.01).$
Therefore, the null hypothesis is rejected at 1% level.
Thus, the results are statistically significant at 1% level of significance.

Interpretation:
Thus, the data provide sufficient evidence to conclude that there is a difference between male and female slot garners with regard to the way they perceive theme as a slot machine attribute at the1%significance level.