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umka2103 [35]
2 years ago
7

Suppose that we are testing H0 : 0 versus H1 : 0 with a sample size of n 10. Calculate bounds on the P-value for the following o

bserved values of the test statistic:
Mathematics
1 answer:
stepan [7]2 years ago
6 0

Answer:

a) p_V = 2*P(t_{9} >|2.48|) =0.0349

We can use the following excel code: "=2*(1-T.DIST(2.48,9,TRUE))"

0.03 < p_v

b) p_V = 2*P(t_{9} >|-3.95|)=0.003355

We can use the following excel code: "=2*(1-T.DIST(3.95,9,TRUE))"

p_v

c) p_V = 2*P(t_{9} >|2.69|) =0.02480

We can use the following excel code: "=2*(1-T.DIST(2.69,9,TRUE))"

0.01 < p_v

d) p_V = 2*P(t_{9} >|1.88|) =0.09281

We can use the following excel code: "=2*(1-T.DIST(1.88,9,TRUE))"

0.05 < p_v

Step-by-step explanation:

For this case we are testing the following system of hypothesis:

Null hypothesis: \mu =0

Alternative hypothesis: \mu \neq 0

The sample size is n=10, so then the degrees of freedom are given by:

df=n-1= 10-1=9

In order to calculate the p value we can use the fact that we are conducting a bilateral test so then the p value is given by:

p_V = 2*P(t_{9} >|t_0|)

Where t_0 represent the calculated or observed statistic.

a) t0= 2.48

p_V = 2*P(t_{9} >|2.48|) =0.0349

We can use the following excel code: "=2*(1-T.DIST(2.48,9,TRUE))"

0.03 < p_v

b) t0= -3.95

p_V = 2*P(t_{9} >|-3.95|)=0.003355

We can use the following excel code: "=2*(1-T.DIST(3.95,9,TRUE))"

p_v

c) t0=2.69

p_V = 2*P(t_{9} >|2.69|) =0.02480

We can use the following excel code: "=2*(1-T.DIST(2.69,9,TRUE))"

0.01 < p_v

d) t0=1.88

p_V = 2*P(t_{9} >|1.88|) =0.09281

We can use the following excel code: "=2*(1-T.DIST(1.88,9,TRUE))"

0.05 < p_v

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