Question

A random sample of 100 observations from a population with standard deviation 6868 yielded a sample mean of 113113. Complete parts a through c below. a. Test the null hypothesis that muμequals=100 against the alternative hypothesis that muμgreater than>​100, using alphaαequals=0.05. Interpret the results of the test. What is the value of the test​ statistic?

Answer 1

Null hypothesis is rejected,

test statistic= 15.76

Explanation:

sample mean= 113,

sample standard deviation= 68

H0: mean of sample =100

Ha: mean of sample > 100

test statistic= (population mean- sample mean)/√(standard deviation/sample size)

test statistic= (113-100)/√(68/100)= 15.76

Degrees of freeedom= 100-1=99

p-value= 1.658 (from t distribution table for DF=99 and alpha=0.05)

Since p-value is smaller than test statistic, null hypothesis is rejected