Step 1 :First, we calculate the test statistic using the formula: \(Z = \frac{M - \mu}{\sigma / \sqrt{n}}\). Here, \(M = 70.2\), \(\mu = 79.5\), \(\sigma = 20.7\), and \(n = 26\).
Step 2 :Substituting the given values into the formula, we get: \(Z = \frac{70.2 - 79.5}{20.7 / \sqrt{26}}\).
Step 3 :Calculating the above expression, we get: \(Z = -2.178\) (rounded to three decimal places). So, the test statistic is \(\boxed{-2.178}\).
Step 4 :Next, we calculate the p-value. The p-value is the probability that a standard normal random variable is less than -2.178 or greater than 2.178.
Step 5 :Using a standard normal table or a calculator, we find that the probability that a standard normal random variable is less than -2.178 is approximately 0.0148.
Step 6 :Since the test is two-tailed, we multiply this probability by 2 to get the p-value. So, the p-value is \(2 \times 0.0148 = 0.0296\) (rounded to four decimal places). So, the p-value is \(\boxed{0.0296}\).
Step 7 :Since the p-value (0.0296) is greater than the significance level (0.01), we fail to reject the null hypothesis \(H_{o}\).