Question

Test the claim below about the mean of the differences for a population of paired data at the level of significance α Assume the samples are random and dependent, and the populations are normally distributed Claim μ,-0: α-0.10. Sample statistics: d-3.5, sd-894, n-9 Identify the null and alternative hypotheses. Choose the correct answer below The test statistic is t (Round to two decimal places as needed) The critical value(s) is(are)- (Round to two decimal places as needed. Use a comma to separate answers as needed.) Since the test statistic isthe rejection region, the null hypothesis. There statistically significant evidence to reject the claim.

Answer 1

Complete Question

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Answer:

The  correct option is F

$t = 1.17$

$t_ {\alpha , df} =t_ {0.10 , 8} = 1.86$

Since the test statistics is outside the rejection region , we fail to reject the null hypothesis ,There is no  statistically significant evidence to reject the claim

Step-by-step explanation:

From the question we are told that

    The  claim is  $\mu = 0$

Hence  

      The  null hypothesis is  $H_o : \mu = 0$

       The  alternative is  $H_a : \mu \ne 0$

Generally the test statistics is mathematically represented as  

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

=>              $t = \frac{3.5 -0 }{ \frac{8.94}{ \sqrt{9} } }$

=>              $t = 1.17$

Generally the degree of freedom is mathematically represented as

      $df = n- 1$

      $df = 9 - 1$

      $df = 8$

From the student t-distribution table  the critical value of  $\alpha$ at a degree of freedom of  8 is  

          $t_ {\alpha , df} =t_ {0.10 , 8} = 1.86$

Since the $t_ {\alpha , df}$ is  outside the rejection region , we fail to reject the null hypothesis ,There is no sufficient evidence to reject the claim