Question 869939: It's believed that that the mean number of dogs owned by dog-owning households is 2.1 dogs. An SRS of 35 dog owners has xbar =2 and s=.29. Carry out an appropriate test to see if the mean number of dogs owned by dog-owning households is something other than 2.1 dogs. Use a 1% level of significance.
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Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Hypothesis:
H0: mu = 2.1
H1: mu =/= 2.1 (mean mu is not equal to 2.1)
This is a two tailed test. So the p value will be visually represented as the area under the curve in both tails
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Test Statistic:
z = (xbar - mu)/(s/sqrt(n))
z = (2-2.1)/(0.29/sqrt(35))
z = -2.04002751141367
z = -2.04
The test statistic is -2.04
Since this value is negative, we are going to be finding the area under the curve to the left of this test statistic.
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P value:
Now use a table to find that the area to the left of z = -2.04 is 0.0207
Double this to get 2*0.0207 = 0.0414 (remember, this is a two tailed test, so the area is symmetrical about the center mean making it in the tips of both tails)
The p value for this two tailed test, and test statistic, is 0.0414
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Comparing the p value with alpha and making a decision:
The p value is 0.0414
The significance level is alpha = 0.01 (note: 1% significance means alpha = 0.01)
The p value is larger than alpha since 0.0414 > 0.01.
This means we fail to reject the null hypothesis H0.
That makes us "accept" the null hypothesis and we must conclude that mu = 2.1
Interpretation: We conclude that the mean number of dogs owned by dog-owning households is 2.1 dogs (as stated initially in the problem, ie this test confirms it).
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