Question

The yields from an ethanol-water distillation column have a standard deviation of 1%. A random sample of eight recent bathes produced these yields 0.90 0.93 0.95 0.86 0.90 0.87 0.93 0.92

For the above 8 observations, the sample mean is 0.9075 and the standard deviation of this sample is s = 0.031.

(a) Construct a 95% confidence interval for the true mean yield.

(b) We are interested in testing H0: µ = 0.95 versus Ha µ ≠ 0.95. Use your result in part a) to check if we reject H0 at α = 0.05 significance level

Answer 1

a)

t critical value at 0.05 level with 7 df = 2.365

95% confidence interval for $\mu$ is

$\bar{x}$ - t * S / sqrt(n) < $\mu$ < $\bar{x}$ + t * S / sqrt(n)

0.9075 - 2.365 * 0.031 / sqrt(8) < $\mu$ < 0.9075 + 2.365 * 0.031 / sqrt(8)

0.8816 < $\mu$ < 0.9334

95% CI is ( 0.8816 , 0.9334 )

b)

Since claimed mean 0.95 is outside the confidence interval, we have sufficient evidence to reject H0.

We conclude at 0.05 level that we have sufficient evidence to support the claim that mean is not 0.95