Get the solution to "The p-value. Given: The size of the sample..."

sibuzwaW

Answered question

2021-09-23

The p-value.
Given: The size of the sample (n) is 15.

Answer & Explanation

Daphne Broadhurst

Skilled2021-09-24Added 109 answers

Explanation: The p-value approach is used to determine whether the null hypothesis can be rejected by using the binomial probability formula.
The binomial probability formula is defined as
$P (X = k) =^{n} C_{k} \times p^{k} \times {(1 - p)}^{n - k}$
where $p = \frac{1}{2}$ for a median test, $X = k$ is the number of positive and negative signs, and n is the total number of plus and minus signs.
The provided data shows that there are 10 observations above the median value of 5.25 and 5 observations below 5.25. Therefore, there are 5 minus signs and 10 plus signs. Thus, n is the total number of plus and minus signs in the data and it is shown below:
$n = 5 + 10$
$= 15$
Since $n = 15 < 25$ , this is a small-sample case and a right-tailed test. The test, statistic, k, is the number of minus signs.
Therefore, the test statistic is $k = 5$ .
The p-value is calculated as follows:
p-value $= P (X \leq k)$
$= P (X \leq 5)$
$= P (X = 0) + P (X = 1) + \dots + P (X = 5)$
$= (^{{15}} C \times {0.5}^{0} \times {(1 - 0.5)}^{15 - 0} +^{15} C \times {0.5}^{1} \times {(1 - 0.5)}^{15 - 1} + \dots +^{15} C \times {0.5}^{5} \times {(1 - 0.5)}^{15 - 5})$
$= (0.00003052 + 0.000458 + 0.003204 + 0.013885 + 0.041656 + 0.091644)$
$= 0.1509$
Therefore, the p-value is obtained as 0.1509.

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