Question

8 of 13 -14 = View Policies Current Attempt in Progress A random sample of 19 observations taken from a population that is normally distributed produced a sample mean of 42.4 and a standard deviation of 8. Find the range for the p-value and the critical and observed values of t for each of the following tests of hypotheses using, a = 0.01. Use the t distribution table to find a range for the p-value. Round your answers for the values of t to three decimal places. a. H: 4 = 46 versus H : 4 < 46. <p-value tcritical 11 tobserved We b. Hou = 46 versus H : # 46. .

Answer 1

We would be looking at the first question all parts here as:

Q1) a) the test statistic here is computed as:

$t^* = \frac{\bar X - \mu_0}{\frac{s}{\sqrt{n}}} = \frac{42.4 - 46}{\frac{8}{\sqrt{19}}} = -1.9615$

Therefore t observed here is -1.9615

As we are testing here whether the mean is less than 46, for n - 1= 18 degrees of freedom , the p-value here is computed from t distribution tables here as:
p = P( t₁₈ < -1.9615) = 0.0327

Therefore 0.0327 is the required p-value here.

For n - 1 = 18 degrees of freedom, we have from t distribution tables here:
P( t₁₈ < -2.552) = 0.01

Therefore -2.552 is the required t critical value here.

As the p-value here is 0.0327 > 0.01 which is the level of significance, therefore the test is not significant here and we cannot reject the null hypothesis here. Therefore we dont have sufficient evidence here that the mean is less than 46 here.