Complete the hypothesis test with alternative hypothesis ƒÊd �‚ 0 based on the paired data that follows and d = O - Y. Use ƒ¿ = 0.01. Assume normality.
Oldest 188 174 192 196 65
Youngest 186 168 199 199 69
(a) Find t. (Give your answer correct to two decimal places.)
-0.52 .
(ii) Find the p-value. (Give your answer correct to four decimal places.)
Can someone give me formula to find p-value, or is there a graph that I should be looking at, my answers are coming up wrong 0.6036
Sorry I have posted this one twice. Just having a lot of problems with getting the p-value and getting discouraged.
The p-value is the actual level of the test statistic you calculate. Since you are calculating t, use a t-table to find the p-value with the appropriate degrees of freedom for the test.
To find the p-value for the hypothesis test with alternative hypothesis f̂d ≠ 0 based on the paired data, you can follow these steps:
1. Calculate the difference for each pair of values: d = O - Y
It seems that you have already done this step for the given data.
2. Calculate the sample mean (X̄) and standard deviation (s) of the differences.
X̄ = mean(d) = sum(d) / n
s = standard deviation of d = √(sum((d - X̄)²) / (n-1))
3. Calculate the test statistic (t) using the formula:
t = (X̄ - μ₀) / (s / √n)
Here, μ₀ represents the hypothesized value for the population mean difference (0 in this case), and n is the number of pairs of data.
In your case, you have already calculated the test statistic (t) to be -0.52, so it seems correct.
4. Determine the degrees of freedom (df) for the t-distribution.
The degrees of freedom for a paired difference test is equal to the number of pairs minus 1 (n - 1).
5. Find the p-value using the t-distribution table or a statistical calculator.
The p-value is the probability of observing a test statistic as extreme as (or more extreme than) the calculated t-value, assuming the null hypothesis is true. When the alternative hypothesis is "not equal to" as in this case, you need to find the p-value for the two-tailed test.
You can use a t-distribution table or a statistical calculator to find the p-value. In this case, since the t-value is already given as -0.52, you can use a t-distribution calculator.
When using a t-distribution calculator, enter the degrees of freedom (df) and the t-value (-0.52), and it will provide you with the corresponding p-value. The desired significance level (α) is 0.01.
Based on the information provided, the p-value is 0.6036 (which you have already calculated). Therefore, if you had set your desired significance level at α = 0.01, since the p-value exceeds α, you would not reject the null hypothesis.