Step 1

According to the provided data, the sample mean is 19.8 and the sample standard deviation is 1.5 and the sample size is 35.

The null and alternative hypotheses are,

\(H_{0}:\mu=19.6\)

\(H_{a}:\mu>19.6\)

This corresponds to a right tailed test.

Step 2

The level of significance is 0.05 and the critical value is obtained as 1.691 for degrees of freedom, \(df = 34 (n – 1)\) using the t-distribution table.

Therefore, the rejection region is t > 1.691.

The t-statistic can be obtained as:

\(t=\frac{\overline{x}-\mu_{0}}{s}/\sqrt{n}=\frac{19.8-19.6}{1.5}/\sqrt{35}=0.789\)

Step 3

Decision: Since, it is observed that \(t = 0.789 < t-critical\ value\ = 1.691\), therefore, the null hypothesis is failed to be rejected.

Using the p-value approach: The p-value is \(p = 0.2178\) using the standard normal table. Since the \(p-value = 0.2178\) is greater than the level of significance = 0.05. The null hypothesis is failed to be rejected.

Therefore, it can be concluded that there is not enough evidence to claim that the mean reflectometer reading greater than 19.6.

According to the provided data, the sample mean is 19.8 and the sample standard deviation is 1.5 and the sample size is 35.

The null and alternative hypotheses are,

\(H_{0}:\mu=19.6\)

\(H_{a}:\mu>19.6\)

This corresponds to a right tailed test.

Step 2

The level of significance is 0.05 and the critical value is obtained as 1.691 for degrees of freedom, \(df = 34 (n – 1)\) using the t-distribution table.

Therefore, the rejection region is t > 1.691.

The t-statistic can be obtained as:

\(t=\frac{\overline{x}-\mu_{0}}{s}/\sqrt{n}=\frac{19.8-19.6}{1.5}/\sqrt{35}=0.789\)

Step 3

Decision: Since, it is observed that \(t = 0.789 < t-critical\ value\ = 1.691\), therefore, the null hypothesis is failed to be rejected.

Using the p-value approach: The p-value is \(p = 0.2178\) using the standard normal table. Since the \(p-value = 0.2178\) is greater than the level of significance = 0.05. The null hypothesis is failed to be rejected.

Therefore, it can be concluded that there is not enough evidence to claim that the mean reflectometer reading greater than 19.6.