ONE SAMPLE T-TEST USING R CONSOLE 

Q. 10 pieces of sarees were selected and number of defects were calculated as: 4, 4,0,3,3,2,3,5,8,6,6

test weather average number of defects on such a cloth is less than 5. 

Sol.

Step I:  we want to test a null hypothesis

                  H0:   mu = 5

against an alternating hypothesis

                  H1:   mu < 5

Step II:  Test statistic
t = x_bar - mu_not/(s/sqrt(n))  ~ t_(n-1)

where s^2=(1/n-1) summation(1 to n)(x_i - x_bar)^2 ~ t_(n-1)

and x_bar = (1/n) summation(1 to n)x_i 

Command used: 

> defect=c(4,0,3,3,2,3,5,8,6,6)
> t.test(defect,alt="less",mu=5)

        One Sample t-test

data:  defect
t = -1.3693, df = 9, p-value = 0.102
alternative hypothesis: true mean is less than 5
95 percent confidence interval:
     -Inf 5.338716
sample estimates:
mean of x
        4

Conclusion:  Since the p-values is greater than 0.05 so we accept the null hypothesis.