Question

The null hypothesis says that a sprinter's reaction time follows a normal distribution with mean at most 0.150 seconds. Six measurements of a sprinter's reaction time show 0.152, 0.154, 0.166, 0.147, 0.161, and 0.159 seconds. What is the p value

Answer 1

Answer:

The P-value is 0.0353.

Step-by-step explanation:

We are given the six measurements of a sprinter's reaction time show below;

X = 0.152, 0.154, 0.166, 0.147, 0.161, and 0.159 seconds.

Let $\mu$ = mean sprinter's reaction time

So, Null Hypothesis, $H_0$ : $\mu \leq$ 0.150 seconds    {means that the mean sprinter's reaction time is at most 0.150 seconds}

Alternate Hypothesis, $H_A$ : $\mu$ > 0.150 seconds    {means that the mean sprinter's reaction time is more than 0.150 seconds}

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

                             T.S.  =    ~  

where, $\bar X$ = sample mean = $\frac{\sum X}{n}$ = $\frac{0.939}{6}$ = 0.1565 seconds

            s = sample standard deviation =  $\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }$ = 0.0068 seconds

            n = sample of measurements = 6

So, the test statistics =  $\frac{0.1565-0.150}{\frac{0.0068}{\sqrt{6} } }$  ~  $t_5$

                                    =  2.341  

The value of t-test statistics is 2.341.

Now, the P-value of the test statistics is given by the following formula;

P-value = P( > 2.341) = 0.0353.

{Interpolating between the critical values at 5% and 2.5% significance level}