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Evgen [1.6K]
2 years ago
7

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

e 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 the mean difference d bar = 3.125, sd = 2.911, and n = 8, and that you wish to test the following hypothesis at the 10% level of significance: H0 : µd = 0 against H1 : µd > 0.
What decision rule would you use? Group of answer choices

a).Reflect H0 if the test statistic is greater than -1.895 and less than 1.896.

b). Reject H0 if test statistic is greater than -1.895.

c). Reject H0 if test statistic is greater than 1.895.

d). Reject H0 if test statistic is less than 1.895
Mathematics
1 answer:
Olegator [25]2 years ago
4 0

Answer:

The critical value for this case can be calculated using the t distribution with 7 degrees of freedom and the critical value would be a value who accumulates 0.1 of the area in the right of the distribution and the best decision based on the possible options would be:

c). Reject H0 if test statistic is greater than 1.895.

Step-by-step explanation:

The system of hypothesis for this case are:

Null hypothesis: \mu_d = 0

Alternative hypothesis: \mu_d >0

The statistic for this case is given by:

t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{3.125 -0}{\frac{2.911}{\sqrt{8}}}=3.04

The degrees of freedom are given by:

df=n-1=8-1=7

The p value for this case can be calculated from this probability:

p_v =P(t_{(7)}>3.4) =0.0057

The critical value for this case can be calculated using the t distribution with 7 degrees of freedom and the critical value would be a value who accumulates 0.1 of the area in the right of the distribution and the best decision based on the possible options would be:

c). Reject H0 if test statistic is greater than 1.895.

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