Assignment 4: T-Test Analysis. Null Hypothesis. Psychology Essay

Assignment 4 – t Tests
Your Name
Course No.
Statistical Methods
Nova Southeastern University
JUNE 29TH, 2018
Assignment 4: T-Test Analysis
One Sample T-test
This assignment is based on a research study which established that American children aged 5 and 12 watched TV on an average time of 196 minutes daily. The study participants were derived through random sampling, where 20 British and American children were sampled. The study set out to determine whether or not the British children in this age bracket were statistically different as compared to their American counterparts based on the amount of television watched per day. This first section will conduct a one sample t-test for the mean.
A one sample t-test was determined to be the most appropriate test that the researchers could use to conduct a comparative analysis of the mean based on a single variable, the daily amount of time spent by British children aged 5 to 12 watching television based on a fixed test value of 196 minutes per day for American children. Based on the presented data, the null hypothesis for the study will be as follows:
Null Hypothesis
H0: The total time spent by British children watching television per night is not statistically different from the test value. Where Null hypothesis presented as (H0), and test value, μ =196.
Alternate Hypothesis
Ha: The total time that British children spent watching television per night is not statistically different from the test value. This is denoted as, Ha: μ ≠ 196.
To conduct a one sample t-test, SPSS version 21 was used, whereas a test value of 196 was used to complete the test. The SPSS output results for the test are tabulated as shown in Figure 1 below.
Figure 1: SPSS output for One Sample t Test –Television watching time
One-Sample Statistics


N

Mean

Std. Deviation

Std. Error Mean

TV watched per night in minutes

20

165.85

29.290

6.550

One-Sample Test


Test Value = 196


t

df

Sig. (2-tailed)

Mean Difference

95% Confidence Interval of the Difference






Lower

Upper

TV watched per night in minutes

-4.603

19

.000

-30.150

-43.86

-16.44

One Sample T-test Mean Analysis
Based on the one sample t test results, it was established that the mean for the British children who watched television daily was 166 (μ = 166). Based on the same results, the t and p values were calculated as follows. The t statistic value was determined as -4.5 whereas the p value was .00. Hypotheses analysis was conducted based on Morgan (2002) where statistical predictions were evaluated for statistical significance. The analysis was based on the null hypothesis, H0 which projected that the total time that British children spent watching television was not statistically different from the test value, μ =196. The test value refers to the daily amount of time that American children spent watching television. The outcome of the one sample t-test analysis significantly varied from the hypothetical projection. This can be represented as follows, t(19) = -4.6, p < .001. The sample t test results further established that the amount of time that British children spent watching television, M=166, SD=29) was significantly less as compared to the test value. This result can be summed up in the following equations:
Time spent watching TV (British Children), (M = 166, SD = 29) < test value (μ = 196).
Hypothesis Analysis
Based on the sample t test results, the null hypothesis (H0) can be rejected and the alternate hypothesis (Ha) accepted. The alternate hypothesis (Ha) is that there exists a statistical disparity between the total time spent by the British children watching television and the test value, μ = 196.
Two samples t-test for evaluating the mean TV watching time equality
The survey utilized a random sample size of, N=20 where American and British children were selected and used to establish the existence of a statistical disparity in the amount of time spent watching television. An independent samples t test is the most suitable test for determining the existing disparity between the means of two separate, but independent variables. In this case, the variables are the daily amount of time that American and British children aged 5 to 12 spent watching television.
The Null Hypothesis:
The total amount of time that British children spend watching television is not statistically different from that of their American counterparts. This can be denoted as H0: μ1 = μ2.
Alternate Hypothesis
The total amount of time that the British children spent watching television is statistically different from that of their American counterparts. This can be denoted as Ha: μ1 ≠ μ2. An independent –samples T-test was conducted on the dataset using SPSS version 21. The output results obtained from the analysis are depicted in Figure 3 ...