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Keith_Richards [23]
3 years ago
11

Determine the decision criterion for rejecting the null hypothesis in the given hypothesis​ test; i.e., describe the values of t

he test statistic that would result in rejection of the null hypothesis. We wish to compare the means of two populations using paired observations. Suppose that d overbar equals​3.125, subscript dequals​2.911, and nequals​8, and that you wish to test the following hypothesis at the​ 10% level of significance. H0​: mu Subscript d equals 0 against H1​: muSubscript dgreater than0 What decision rule would you​ use?
Mathematics
1 answer:
slega [8]3 years ago
7 0

Answer:

t = \frac{3.125-0}{\frac{2.911}{\sqrt{8}}}= 3.036

We can use the p value as a decision rule is p_v we reject the null hypothesis.

Now we can find the degrees of freedom given by:

df = n-1=8-1=7

And the p value would be:

p_v = P(t_{7} >3.036) = 0.0094

And since the p_v we have enough evidence to reject the null hypothesis in favor to the alternative hypothesis.

Step-by-step explanation:

For this case we have the following statistics for the difference between the paired observations:

\bar d = 3.125 the sample mean for the paired difference

s_d = 2.911 the sample deviation for the paired difference data

n =8 the sample size

The system of hypothesis that we want to check is:

Null hypothesis: \mu_d =0

Alternative hypothesis: \mu_d > 0

And the statistic is given by:

t = \frac{\bar d -\mu_d}{\frac{s_d}{\sqrt{n}}}

And replacing we got:

t = \frac{3.125-0}{\frac{2.911}{\sqrt{8}}}= 3.036

We can use the p value as a decision rule is p_v we reject the null hypothesis.

Now we can find the degrees of freedom given by:

df = n-1=8-1=7

And the p value would be:

p_v = P(t_{7} >3.036) = 0.0094

And since the p_v we have enough evidence to reject the null hypothesis in favor to the alternative hypothesis.

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