Question

In Problems 1 - 3, assume that the population of x values has an approximately normal distribution. Answers may vary slightly due to rounding to TWO decimals:

(a) What is the level of significance? State the null and alternate hypothesis. (b) What sample distribution will use? Write the formula for test statistic and find the value? (c) Find the P-Value of the test statistic. (d) Sketch the graph of sampling distribution and show the area corresponding to P-Value. (e) Based on your answers in parts (a) to (d), will you reject or fail to reject the null hypothesis? (f) Interpret your conclusion in the context of the application.

1. A researcher wishes to determine whether there is a relationship between the gender of an individual and the amount of alcohol consumed. A sample of 68 people is selected, and the following data are obtained. At ∝ =0.10 , can the researcher conclude that alcohol consumption is related to gender?                                                           (15 – Pts)                  

                                                                                               

Gender	Low	Moderate	High	Total
Male	10	9	8
Female	13	16	12
Total

           

Answer 1

Answer a)

The level of significance is 0.10

The null and alternate hypothesis are:

H0: There is a no relationship between the gender of an individual and the amount of alcohol consumed

H1: There is a relationship between the gender of an individual and the amount of alcohol consumed

Answer b)

The Chi square distribution will be used

The formula of Chi square statistic is as follows:

Answer c)

The number of degrees of freedom is df = (r-1)*(c-1) = (2−1)*(3−1) = 2

The p-value corresponding to test statistic = 0.281 and df = 2 is obtained using p-value calculator. Screenshot below:

Thus, P-value = 0.8690

Answer d)

The graph of sampling distribution and show the area corresponding to P-Value

Answer e)

Since p-value = 0.8690 > ∝ = 0.10, we fail to reject null hypothesis.

Answer f)

Conclusion

At 0.10 significance level, there is not enough evidence to support the claim that there is a relationship between the gender of an individual and the amount of alcohol consumed