Question

A famous cable company conducted an analysis to test gender differences in # of hours spent watching TV per day. In particular, the company tested whether men spent more time on watching TV than women. A T-test was conducted utilizing normally distributed random sample data at a=0.05.  

Women	Men
1	0	t-Test: Two-Sample Assuming Unequal Variances
1	1
1	1		Variable 1	Variable 2
2	2	Mean	3.214286	3.3
2	2	Variance	7.873626	11.34444
2	3	Observations	14	10
2	4	Hypothesized Mean Difference	0
3	4	df	17
3	4	t Stat	-0.0658
3	12	P(T<=t) one-tail	0.474152
4		t Critical one-tail	1.739607
4		P(T<=t) two-tail	0.948304
5		t Critical two-tail	2.109816
12

Answer the following questions based on the data and the t-test provided above. Be sure to report your answers in sentence form (15 pts).

1. What are the alternate hypothesis and the null hypothesis (2 pts)?
2. Check whether t-test assumptions are met. If applicable, identify methods utilized by the company for testing assumptions (6 pts)?   
3. Identify, critical values of the T-test (3 pts).
4. Draw a conclusion (Utilize t-test statistics, C.V. and P-value) (4 pts)?

Answer 1

(1)

Sample 1 = Women

Sample 2 = Men
H0: Null Hypothesis: (Men do not spend more time on watching TV than women)

HA: Alternative Hypothesis: (Men spend more time on watching TV than women) (Claim)

(2)

Conditions for 2 Independent Samples t test:

(i) The dependent variable is continuous: Here, hours spent is a continuous variable.

(ii) The independent variable is categorical. Here, Gender is a categorical variable.

(iii) Independence of observations: There is no relationship between the observations in each group or between the groups themselves.

(iv) Random samples of data from the population

(v) Normal distribution of the dependent variable

(vi) Variances are approximately equal across groups

(vii) There are no significant outliers.

(3)

Critical values of the t test are given by:

- 1.739607

(4)

Since the calculated value of t = - 0.0658 is greater than critical value of t = - 1.739607, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that Men spend more time on watching TV than women.

Since the p value = 0.474152 is greater than critical value of = 0.05, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that Men spend more time on watching TV than women.