use technology to find the P-value for a two tailed test with n=28 and a test statistic t=2.032
P-value =????
Help please! i don't understand this
P value is the probability that the results were do solely to chance. P = .05 means that the probability that the results were due solely to chance were 5 times in 100. Depending on your tolerance for occurring by chance, you will reject the null hypothesis if P is too small.
For P ≤ .05, the t value with 27 df = 2.052.
df = n - 1
Melissa has scored
83
,
72
,
89
,
64
, and
94
on her previous five tests. What score does she need on her next test so that her average (mean) is
82
?
To find the p-value for a two-tailed test with the given information, you need to utilize a statistical software or calculator that can compute the p-value using the t-distribution.
Here's how you can calculate the p-value using common statistical software like R or Python:
Using R:
1. Open R or RStudio.
2. Type the following command: `pt(2.032, df = 27)*2`
- `pt` is the function to calculate the cumulative probability of the t-distribution.
- `2.032` is the value of the test statistic.
- `df = 27` is the degrees of freedom, which is equal to n - 1.
- `*2` is to account for the two-tailed test.
3. Press Enter, and you will get the p-value.
Using Python:
1. Open a Python environment like Jupyter Notebook or Anaconda.
2. In the code cell, type the following commands:
```python
import scipy.stats as stats
p_value = stats.t.sf(2.032, df=27)*2
print(p_value)
```
- `stats.t.sf` is the function to calculate the survival function (1 - cumulative probability) of the t-distribution.
- `2.032` is the value of the test statistic.
- `df = 27` is the degrees of freedom, which is equal to n - 1.
- `*2` is to account for the two-tailed test.
3. Run the code cell, and you will get the p-value printed.
The p-value represents the probability of obtaining a test statistic as extreme as the one observed (or more extreme) if the null hypothesis is true. Lower p-values indicate stronger evidence against the null hypothesis.
Note: The calculation may vary depending on the statistical software or programming language you use, but the concept remains the same.