Answer to Question #346609 in Statistics and Probability for kai

Question

A manufacturing firm claims that each water bottle they produce contains an average of 300 mL of water with a standard deviation of 1.2 mL. A random sample of 20 water bottles showed an average volume of 301.4 mL. if the t-value in the test is 3.14 and the critical values are ±2.861, what is the appropriate decision conclusion in the hypothesis testing?

Answer 1

The following null and alternative hypotheses need to be tested:

$H_0:\mu=300$

$H_1:\mu\not=300$

This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used.

The rejection region for this two-tailed test is $R = \{t:|t|>2.861\}.$

The t-statistic is $t=3.14.$

Since it is observed that $|t|=3.14>2.861=t_c,$ it is then concluded that the null hypothesis is rejected.

Therefore, there is enough evidence to claim that the population mean $\mu$

is different than 300.