Question 1041394: 60 61 64 62 64 62 60 60.5 67 66
63 62 64.5 63.5 63 62 65 66 63 67
Test the hypothesis that dancers have a smaller population mean height than 64.5″ at the 0.05 significance level.
(a) State the null& alternative hypotheses.
H0:
Ha:
p-value = ________
Decision: __________ (Reject, Fail to reject) H0.
Answer the questions: At the 0.05 significance level, do the data provide sufficient evidence that dancers have a smaller population mean height than 64.5″?
If the significance level is 0.01, what would be the decision and
interpretation?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Null hypothesis is dancers have a height >=64.5 inches
Alternative hypothesis is that their height is <64.5 inches
This is a one sample t-test
the mean is 63.275 and s=2.167
It is a t-test with 19 df and the p-value is 0.010. The numerical value of the t is -2.528, which is less than the critical value of t=-1.729. That can be found in a t-table with 19 df, one way, where the 0.05 is all in one direction.
Reject Ho at the 5% level and conclude that there the dancers have a smaller population height than 64.5 inches.
Were the significance level 0.01, it would be close but one would fail to reject the null hypothesis.
The interpretation in the first is that dancers are shorter.
The interpretation in the second is that they are not shorter. Sometimes, people will put "a trend" in the report, but they either are or aren't. What one can do is suggest a larger sample size, which is one way to show a significant difference, assuming the mean and the sd don't change.
The question has apparently been to give a numerical result. I have, unless a confidence interval is additionally required. I have given the p-value and the t-value.
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