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

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 \\e 0`

Generally the test statistics is mathematically represented as

`t = (\= d - \mu_d )/( (s_d)/( √(n) ) )`

=>
`t = (3.5 -0 )/( (8.94)/( √(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