How do I figure out the critical value for a test from the alpha value?
Lube-Tech is a major chain whose primary business is performing lube and oil changes for passengers vehicles. The national operations manager has stated in an industry newsletter that the mean number of miles between oil changes for all passengers cars exceeds 4,200 miles. To test this, an industry group has selected a random sample of 100 vehicles that have come into a lube shop and determined the number of miles since the last oil change and lube. The sample mean was 4,278 and the sample standard deviation was known to be 780 miles. Based on a significance level of 0.10, the critical value for the test is approximately _____
I got 1.645..just from looking in my book..but apparently thats wrong. What do I do?
Since the sample size is 100, then the sample standard deviation is a reasonable estimate of the population standard deviation. The standard error (standard deviation of sample means) is
population standard deviation/square root sample size = 780/10 = 78
In this test the null hypothesis is mean mileage between oil changes is 4200.
The alternative hypothesis is mean mileage between oil changes is greater than 4200.
This means that it is a one-tailed test for high values.
With a one-tailed test at 10% significance level the figure is z >= 1.28
The observed result of 4278 is 1 standard error over the mean so it is not a significant.
Conclusion - there is not enough evidence to assume that mileage between oil changes is greater than 4200.
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