No idea where to begin...
Do men or women watch more T.V. per day? To answer the question two samples were select with the help of SPSS and the following results were produced. Is there a significant difference between men and women in watching T.V.? Perform five-step model to test the hypothesis.
Descriptive Statisticsa
N Mean Std. Deviation
HOURS 86 2.56 2.324
Valid N (listwise) 86
a. RESPONDENTS SEX = MALE
Descriptive Statisticsa
N Mean Std. Deviation
HOURS 96 3.01 2.269
Valid N (listwise) 96
Don't know what you call "five-step model," but here is a method.
Z = (mean1 - mean2)/standard error (SE) of difference between means
SEdiff = √(SEmean1^2 + SEmean2^2)
SEm = SD/√n
If only one SD is provided, you can use just that to determine SEdiff.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
To test whether there is a significant difference between men and women in watching TV, you can use a t-test. The five-step model to test the hypothesis includes:
Step 1: State the hypothesis
- Null Hypothesis (H0): There is no significant difference between men and women in watching TV.
- Alternative Hypothesis (Ha): There is a significant difference between men and women in watching TV.
Step 2: Set the significance level (alpha)
- The significance level, also known as alpha (α), is the probability of rejecting the null hypothesis when it is true. Commonly used values for alpha are 0.05 and 0.01, which represent a 5% and 1% chance, respectively, of rejecting the null hypothesis even if it is true.
Step 3: Compute the test statistic
- In this case, you will use an independent samples t-test, assuming that the two samples (men and women) are independent of each other.
- The test statistic for an independent samples t-test is calculated as t = (mean of group 1 - mean of group 2) / (standard error).
- The standard error is calculated as the square root of ((variance of group 1 / size of group 1) + (variance of group 2 / size of group 2)).
- In this scenario, group 1 refers to men and group 2 refers to women.
Step 4: Determine the critical value
- The critical value is the value beyond which we would reject the null hypothesis.
- The critical value can be obtained from a t-distribution table, given the degrees of freedom and the significance level.
- The degree of freedom (df) can be calculated as (size of group 1 + size of group 2) - 2.
Step 5: Make a decision
- Compare the calculated test statistic with the critical value.
- If the calculated test statistic is greater than the critical value, reject the null hypothesis; otherwise, fail to reject it.
- If the null hypothesis is rejected, it implies that there is a significant difference between men and women in watching TV.
Now, let's calculate the test statistics based on the provided data:
For men:
- Sample size (N) = 86
- Mean (M) = 2.56
- Standard deviation (SD) = 2.324
For women:
- Sample size (N) = 96
- Mean (M) = 3.01
- Standard deviation (SD) = 2.269
1. Compute the test statistic:
- Difference in means = (mean of men) - (mean of women) = 2.56 - 3.01 = -0.45
- Standard error = sqrt((SD^2_men / N_men) + (SD^2_women / N_women))
= sqrt((2.324^2 / 86) + (2.269^2 / 96))
= sqrt(0.055 + 0.051)
≈ sqrt(0.106)
≈ 0.3267
- t-value = (difference in means) / (standard error)
= -0.45 / 0.3267
≈ -1.3777
2. Determine the critical value:
- Degree of freedom (df) = (N_men + N_women) - 2
= (86 + 96) - 2
= 180 - 2
= 178
- Using a t-distribution table or a statistical software, find the critical value for a two-tailed test with a significance level of 0.05 and 178 degrees of freedom. Let's assume it is -1.96.
3. Make a decision:
- Since the calculated t-value (-1.3777) is greater than the critical value (-1.96) for a significance level of 0.05, we fail to reject the null hypothesis.
- Therefore, based on the data provided, there is no significant difference between men and women in watching TV.