Question

1)     Professor Barson wants to know if his advanced statistics class has a good grasp of basic math. Six students are chosen at random from the class and given a math proficiency test. The six students get scores of 62, 92, 75, 68, 83, and 90.

a.     Conduct a hypothesis test to see whether the mean score from this year’s class is different than last year’s class mean of 80. Then, construct a 95% confidence interval for this year’s class mean.

Answer 1

solution:

first of all calculating the mean and standard deviation of sample data as shown below:

sample mean =

sd =

null and alternativ e hypothesis:

since population standard deviation is not known so we use t-distribution

test statistics:

let

degree of freedom = df = n-1 = 6-1 = 5

so, critical value of t from t table as follows:

since t=-0.339 > -2.571 , so null hypothesis is not rejected

conclusion:

do not reject the null hypothesis, and concluded that the mean score of students is not different the score of previous year i,e, 80 .

b)

confidence interval

confidence level = 95% = 0.95

margin of error :

confidence interval =

so upper limit = 78.33 + 12.68 = 91.01

lower limit = 78.33 - 12.68 = 65.65

so confidence interval = (65.65 , 91.01)