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.
a. What test should he use?
b. What is the alternative hypothesis?
c. What is the null hypothesis?
d. What is the critical value?
e. What is the obtained statistic?
f. What should he conclude?

Answer 1

Answer:

a) one sample t-test

b) mean of sample≠ mean of population

c)mean of sample= mean of population

d) 2.045

e) 2.510395

f) null hyptohesis is rejected

Explanation:

a) one sample t-test is used to compare known or hypothesized population mean with sample mean

b) H1:mean of sample≠ mean of population

c) H0: mean of sample= mean of population

d) for df=30-1=29 and alpha = 0.05

p-value= 2.045

e) t-statistic= (sample mean-population mean)/estimated standard error of mean

estimated standard error of mean= sample mean/√sample size

esitmated standard error of mean= 7.3/√30

                                                         = 0.438178046

t-statistic= (7.3-6.2)/ 0.438178046

              = 2.510

f) since t-statistic is greater than p-value, null hypothesis is rejected