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

The P-value is 0.0353.

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 =
`(\sum X)/(n)` =
`(0.939)/(6)` = 0.1565 seconds

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

n = sample of measurements = 6

So, the test statistics =
`(0.1565-0.150)/((0.0068)/(√(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}