In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is $\textbf{ not }$ equal to 4.8, a random sample of 25 items is selected. The sample mean is 4.1 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The level of significance is selected to be 0.10. The critical t value for this problem is ___.
A) 1.318
B) 1.711
C) 2.492
D) 2.797
E) 3.227

Question

In performing a hypothesis test where the null hypothesis is that the population mean is 4.8 against the alternative hypothesis that the population mean is $\textbf{      not   }$  equal to 4.8, a random sample of 25 items is selected. The sample mean is 4.1 and the sample standard deviation is 1.4. It can be assumed that the population is normally distributed. The level of significance is selected to be 0.10. The critical t value for this problem is ___.
A) 1.318
B) 1.711
C) 2.492
D) 2.797
E) 3.227

Quizplus · Accepted Answer

To find the critical t-value, we first need to calculate the degrees of freedom (df), which is n-1=24.

Since the alternative hypothesis is two-tailed, we divide the level of significance by 2 to get the area in each tail: 0.10/2 = 0.05.

Using the t-table or a calculator, we can find the t-value that corresponds to a cumulative area of 0.05 in the upper tail with 24 degrees of freedom: t = 1.711.

Since the alternative hypothesis is not equal to 4.8, we need to find the critical t-value in both tails by multiplying the one-tailed t-value by -1: -1.711.

Therefore, the critical t-value for this problem is 1.711 (or -1.711).

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

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