Question 1186795: Assume that a simple random sample has been selected from a normally distributed population. Find the test statistic t.
Test the claim that the mean lifetime of a particular car engine is greater than 220,000 miles. Sample data are summarized as n = 23, x-bar = 226,450 and s=11,500. Use a significance level of 5%. Find the test statistic t.
2.69
-2.69
2.24
-2.24
12.9
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Here's how to calculate the test statistic t:
1. **Identify the given values:**
* n (sample size) = 23
* x̄ (sample mean) = 226,450 miles
* s (sample standard deviation) = 11,500 miles
* μ (population mean under the null hypothesis) = 220,000 miles
2. **Use the formula for the t-statistic:**
t = (x̄ - μ) / (s / √n)
3. **Plug in the values:**
t = (226,450 - 220,000) / (11,500 / √23)
t = 6,450 / (11,500 / 4.7958)
t = 6,450 / 2400.05
t ≈ 2.687
Rounding to two decimal places, the test statistic *t* is approximately 2.69.
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