Michael D. answered • 07/31/23
Maths, Stats, and CompSci Tutoring from a former University Professor
This is a Hypothesis Test about a single population mean; the Null Hypothesis says the population mean is equal to 13.74. Since we don't know the population's standard deviation, we'll be using the Student-T distribution for the test statistic. The question asks whether we can conclude the mean length is *different from* 13.74, which is a two-sided/tailed test.
We need to compute:
* Standard Error = [Sample Standard Deviation]/sqrt([Sample Size]) = 0.198...
* Test Statistic = ([Sample Mean] - [Hypothesized Mean])/[Standard Error] = 4.738...
The Degrees of Freedom in this case is [Sample Size] - 1 = 149.
- Using the Critical Value/Region Method (from a table of values), the critical value for a two-tailed T-distribution with df = 149 at 2% significance level is 2.352... The absolute value of our test statistic is larger, so Reject the Null Hypothesis.
- Using the P-value method (with technology), the one-sided P-value is the area to the right of t = 4.378 (in the T distribution with df = 149), which is effectively zero. Double this to get the two-sided P-value (still effectively zero). Since 0 = 0% is less than the 2% significance level, Reject the Null Hypothesis.
Either way, we Reject the Null Hypothesis. So can conclude the population mean is different from 14.73.
(There appears to be an error in the wording of the problem. The last sentence mentions phone calls instead of vet clinics. I'm not going to speculate why this occurred, but it doesn't affect the computations above).
