Question

Dr. Vegapunk thinks that watching anime (Japanese animated shows) decreases social skills in college students. To test this, Dr. Vegapunk randomly selected 30 brooklyn college students and assigned them to watch an episode of anime everyday for a week. After the week, each of the students answered a questionnaire about their social skills. The results showed that the sample had a mean social skills score of 7.3 and a standard deviation of 2.4. A previous study showed that the overall population of brooklyn college students had a mean social skills score of 6.2, but the standard deviation was not reported. Dr. Vegapunk decides to use an alpha level of 0.05

what is the critical value

what is the obtained statistic

what should he conclude

Answer 1

null hypothesis: HO: μ		=	6.2
Alternate Hypothesis: Ha: μ		<	6.2
0.05 level with left tail test and n-1= 29 df, critical t=				-1.699 (use tinv(0.05*2,29) function from excel)

population mean μ=	6.2
sample mean 'x̄=	7.300
sample size   n=	30.00
sample std deviation s=	2.400
std error 'sx=s/√n=2.4/√30 =	0.4382
test stat t ='(x-μ)*√n/sx=(7.3-6.2)/0.4382 =	2.510

since test statistic does not falls in rejection region we fail to reject null hypothesis
we do not have have sufficient evidence to conclude that  watching anime decreases social skills in college students. .

even it appears from sample that student who watches anime has higher mean score from population