Question

A study is done to see if the average age a "child" moves permanently out of his parents' home in the United States is at most 23. 43 U.S. Adults were surveyed. The sample average age was 24.2 with a standard deviation of 3.7. The p-value is

Answer 1

Answer:

The p-value is 2.1%.

Step-by-step explanation:

We are given that a study is done to see if the average age a "child" moves permanently out of his parents' home in the United States is at most 23. 43 U.S. Adults were surveyed.

The sample average age was 24.2 with a standard deviation of 3.7.

Let $\mu$ = true average age a "child" moves permanently out of his parents' home in the United States.

So, Null Hypothesis, $H_0$ : $\mu \leq$ 23      {means that the average age a "child" moves permanently out of his parents' home in the United States is at most 23}

Alternate Hypothesis, $H_A$ : $\mu$ > 23      {means that the average age a "child" moves permanently out of his parents' home in the United States is greater than 23}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                            T.S.  =  $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$  ~ $t_n_-_1$

where, $\bar X$ = sample average age = 24.2

            s = sample standard deviation =3.7

            n = sample of U.S. Adults = 43

So, the test statistics =  $\frac{24.2-23}{\frac{3.7}{\sqrt{43} } }$  ~  $t_4_2$

                                    =  2.127

The value of t-test statistics is 2.127.

Now, the p-value of the test statistics is given by;

         P-value = P( $t_4_2$ > 2.127) = 0.021 or 2.1%