Question

The desired percentage of silicon dioxide in a certain type of cement is 5. A random sample of 36 specimens gave a sample average percentage of 5.21 and a sample standard deviation of 0.38. Use a significance level of 0.01 and test whether the sample result indicates a change in the average percentage.

Answer 1

Answer on Question #42678 – Math - Statistics and Probability

The desired percentage of silicon dioxide in a certain type of cement is 5. A random sample of 36 specimens gave a sample average percentage of 5.21 and a sample standard deviation of 0.38. Use a significance level of 0.01 and test whether the sample result indicates a change in the average percentage.

Solution

$$H_0: \mu = 5 \quad H_A: \mu \neq 5 \quad \alpha = 0.01$$

The alternative hypothesis is $\neq$, indicating a two-tail test. The Central Limit Theorem applies therefore we use z-distribution.

Reject $H_0$ if z-test > 2.58 or z-test < -2.58.

$$z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} = \frac{5.21 - 5.0}{\frac{0.38}{\sqrt{36}}} = 3.32.$$

Since $3.32 > 2.58$ we reject $H_0$ at the 0.01 level of significance. The sample evidence does suggest that there is a significant change in the average percentage of silicone dioxide in a certain type of cement.

www.AssignmentExpert.com