Question

You are testing $H_0:\mu =10$against $H_a:\mu <10$based on an SRS of$20$

observations from a Normal population. The t statistic is $t=-2.25$

The $P-$value

a. falls between 0.01 and 0.02.

b. falls between 0.02 and 0.04.

c. falls between 0.04 and 0.05.

d. falls between 0.05 and 0.25.

e. is greater than 0.25.

Short answer

The correct option is (a) falls between falls between $0.01$ and $0.02$

Step-by-step solution

Given information

Sample size$\left(n\right)=20$

Test statistic$\left(t\right)=-2.25$

The null and alternative hypotheses are:

$$\begin{gathered} H_0:\mu =10 \\ {H}_a:\mu <10 \end{gathered}$$

Explanation

According to the alternative hypothesis, the test is one-tailed.

The degree of freedom can be determined using the following formula:

$$\begin{gathered} Degreeoffreedom(df)=n-1 \\ =20-1 \\ =19 \end{gathered}$$

The $p-$value can be calculated as:

$$\begin{gathered} P-value=P(t>|t\left|\right) \\ =P(t>|-2.25\left|\right) \\ =0.018 \end{gathered}$$

Thus, it could be said that $P-$value lies between$0.01and0.02$

Hence, the correct option is (a).