If it’s relatively riskier to reject the null hypothesis when it might be true, should a smaller or a larger significance level be used?

If it is relatively riskier to reject the null hypothesis when it might be true, a smaller significance level should be used.

Step-by-step explanation:

Rejecting the null hypothesis when it is true is a Type I error.

In hypothesis test, p-value of test statistics is used to compare against significance level.

If p-value < significance level (p-value is smaller than significance level) then the result would be significant and the null hypothesis is rejected.  

To reduce the probability of rejecting the null hypothesis, the chances of the  p-value being smaller than significance level has to be reduced.

For smaller significance level, the chance of p-value < significance level reduces, therefore smaller significance level decreases the risk of the null hypothesis being rejected.

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

$25

step-by-step explanation:

25 - 4.50 = 20.5

20.5 / 2 = 10.25

10.25 + 10 = 20.25

20.25 - 12.50 = 7.75

therefore the answer is $25 as shown as the first number.