# True, False, or Uncertain. In each of the following situations, state whether each statement is true,false, or uncertain, and explain your answer. Your score is evaluated on the explanation you providetherefore, if you do not provide explanation, you will not receive any credit even if you stated truefalse, or uncertain correctly1.As the degrees of freedom k decrease, the t distribution density curve gets closer to the N(0,1)curvea.The standard error of the sample mean is s'/nb.A researcher wants to test Ho:= 30 versus the one sided alternative Ha:< 30c.d.The 95% margin of error for the mean u of a Normal population with unknown o is the samefor all SRS of size n.

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Step 1

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Step 2

a. False,

As the degrees of freedom increases, the t-distribution approaches normality. This means that, the area near the center increases while the area near the tail decreases.  When the degrees of freedom decreases, the area near the center decreases while the area near the tail increases. Or otherwise, as the degrees of freedom increases, the sample size increases and thus, the sample approaches the population.

Thus, the statement that ‘As the degrees of freedom k decrease, the t distribution density curve gets closer to the N(0,1) curve’ is False.

Step 3

b. False,

The standard error of the mean obtained by dividing the sample standard deviation with the square root of sample size. That is, SE= s/sqrt(n).

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