The best approximation for the p-value for the test statistic is 0.005775
Finding the best approximation for the p-value for the test statistic
To find the approximation for the p-value, we need to calculate the t-statistic
And then use it to determine the corresponding p-value using a t-distribution table
The t-statistic is calculated as:
t = (x - μ) / (s / √n)
Where:
- x is the sample mean
- μ is the hypothesized mean (10 in this case)
- s is the sample standard deviation
- n is the sample size (10 in this case)
Assume the sample mean is 8 and sample standard deviation (s) is 2, we have
t = (8 - 10) / (2 / √10) = -3.16
Since H1 is one-tailed (μ < 10), we need to find the area to the left of the t-statistic in the t-distribution table with degrees of freedom (df) = n - 1 = 10 - 1 = 9.
Using a t-distribution table, we find that the p-value is approximately 0.005775