Question 1186800: 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 Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
assumed population mean = 220000
sample mean = 226450
sample standard deviation is 11500
sample size is 23
t-score = (x - m) / s
x is the sample mean
m is the population mean
s is the standard error
the standard error = sample standard deviation divided by square root of sample size = 11500 / sqrt(23) = 2397.95762.
t-score = (226450 - 220000) / 2397.95762.
t-score = 2.69 rounded to 2 decimal places.
that's your first selection.
since your test is greater than, you need a one-tail significance level of .05.
the critical t-score at 22 degrees of freedom (sample size of 23 minus 1 = 22), is 1.72 rounded to 2 decimal laces.
since your test t-score is greater than this, you would make the claim that the mean lifetime of that particular engine is greater than 220,000 miles.
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