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

sibuzwaW

sibuzwaW

Answered question

2021-09-23

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

Answer & Explanation

Daphne Broadhurst

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)=nCk×pk×(1p)nk
where p=12 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(Xk)
=P(X5)
=P(X=0)+P(X=1)++P(X=5)
=({15}C×0.50×(10.5)150+15C×0.51×(10.5)151++15C×0.55×(10.5)155)
=(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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