Question

 

A researcher is interested to learn if there is a relationship between the level of interaction a women in her 20s has with her mother and her life satisfaction ranking. Below is a list of women who fit into each of four level of interaction. Conduct a One-Way ANOVA on the data to determine if a relationship exists.

 

No Interaction	Low Interaction	Moderate Interaction	High Interaction
2	3	3	9
4	3	10	10
4	5	2	8
4	1	1	5
7	2	2	8
8	2	3	4

 

 

 

1	7	10	9
1	8	8	4
8	6	4	1
4	5	3	8

 

Is there a relationship between handedness and gender? A researcher collected the following data in hopes of discovering if handedness and gender are independent (Ambidextrous individuals were excluded from the study). Use the Chi-Square test for independence to explore this at a level of significance of 0.05.

 

 

	Left-Handed	Right-Handed
Men	13	22
Women	27	18

 

A researcher is interested in studying the effect that the amount of fat in the diet and amount of exercise has on the mental acuity of middle-aged women. The researcher used three different treatment levels for the diet and two levels for the exercise. The results of the acuity test for the subjects in the different treatment levels are shown below.

	Diet
Exercise	<30% fat	30% - 60% fat	>60% fat
<60 minutes	4	3	2
	4	1	2
	2	2	2
	4	2	2
	3	3	1
60 minutes	6	8	5
or more	5	8	7
	4	7	5
	4	8	5
	5	6	6

 

 

 

 

 

Answer 1

Solution:-

1)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: ?₁ = ?₂ = ?₃ = ?₄

Alternative hypothesis: At-least one of the ? is not equal.

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data.

F statistics is given by:-

F = 1.57

F_critical = 2.87

The P-value = 0.21

Interpret results. Since the P-value (0.21) is greater than the significance level (0.05), we have to accept the null hypothesis.

Conclusion:-

Reject H₀, There is not sufficient evidence for significant differences between the four groups.

2)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

H₀: Handedness and gender are independent.
H_a: Handedness and gender are not independent.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square test for independence.

Analyze sample data. Applying the chi-square test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

DF = (r - 1) * (c - 1) = (2 - 1) * (2 - 1)
D.F = 1
E_r,c = (n_r * n_c) / n

?² = ? [ (O_r,c - E_r,c)² / E_r,c ]
?² = 4.114

where DF is the degrees of freedom.

The P-value is the probability that a chi-square statistic having 1 degrees of freedom is more extreme than 4.114.

We use the Chi-Square Distribution Calculator to find P(?² > 4.114) = 0.0425

Interpret results. Since the P-value (0.0425) is less than the significance level (0.05), we cannot accept the null hypothesis.

Thus, we conclude that there is a relationship between Handedness and gender.