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.

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 [tex]\mu = 0[/tex]

Hence

The null hypothesis is [tex]H_o : \mu = 0[/tex]

The alternative is [tex]H_a : \mu \ne 0[/tex]

Generally the test statistics is mathematically represented as

[tex]t = \frac{\= d - \mu_d }{ \frac{s_d}{ \sqrt{n} } }[/tex]

=> [tex]t = \frac{3.5 -0 }{ \frac{8.94}{ \sqrt{9} } }[/tex]

=> [tex]t = 1.17[/tex]

Generally the degree of freedom is mathematically represented as

[tex]df = n- 1[/tex]

[tex]df = 9 - 1[/tex]

[tex]df = 8[/tex]

From the student t-distribution table the critical value of [tex]\alpha[/tex] at a degree of freedom of 8 is

[tex]t_ {\alpha , df} =t_ {0.10 , 8} = 1.86[/tex]

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