1. T-test for a single sample You administer a survey of happiness to a sample of N = 4 students taking PSY-3205. The survey measures happiness on a 7-point Likert scale, with 4 being the happiness scale neutral mid-point (neither happy nor unhappy), 1 being very unhappy and 7 being very happy. You want to determine if the mean score measured from your population differs significantly from the neutral mid-point of 4.

Student ;Happiness Score
1 ; 2
2 ; 1
3 ; 2
4 ; 3

a) State the null hypothesis (H0) and the research hypothesis (H1)

b) Compute the sample mean M

c) Compute the degrees of freedom (df)

d) Fill out the following table and then estimate the population standard deviation (s)

X M X-M (X-M)2

2
1
2
3

SS:

Remember, s2 = SS/df

e) Write the expression for your T-statistic, and plug in the numbers to compute the t-score

f) Using your T-score table, for a 2-tailed test is your observation significant at the level of p<0.05? How about p < 0.01?

g) Compute Cohen’s d

h) What is the 95% confidence interval for the true population mean?