In performing a hypothesis test where the null hypothesis is that the population mean is 6.9 against the alternative hypothesis that the population mean is $\textbf{ not }$ equal to 6.9, a random sample of 16 items is selected. The sample mean is 7.1 and the sample standard deviation is 2.4. It can be assumed that the population is normally distributed. The level of significance is selected as 0.05. The critical t value for this problem is ___.
A) 1.753
B) 2.947
C) 2.120
D) 2.131
E) 2.311

Question

In performing a hypothesis test where the null hypothesis is that the population mean is 6.9 against the alternative hypothesis that the population mean is $\textbf{   not      }$  equal to 6.9, a random sample of 16 items is selected. The sample mean is 7.1 and the sample standard deviation is 2.4. It can be assumed that the population is normally distributed. The level of significance is selected as 0.05. The critical t value for this problem is ___.
A) 1.753
B) 2.947
C) 2.120
D) 2.131
E) 2.311

Quizplus · Accepted Answer

The critical t value can be found using a t-distribution table with (n-1) degrees of freedom and a level of significance of 0.05. In this problem, the degrees of freedom are 16-1=15. Therefore, the critical t value will be the t-value that gives an area of 0.025 in both tails of the distribution. From the t-distribution table, the critical t value with 15 degrees of freedom and a two-tailed alpha of 0.05 is 2.131. Thus, the answer is D.

In Performing a Hypothesis Test Where the Null Hypothesis Is not \textbf{ not } not

In Performing a Hypothesis Test Where the Null Hypothesis Is $\textbf{ not }$