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Inessa [10]
3 years ago
6

1) If the alpha level is changed from α = .05 to α = .01, what happens to boundaries for the critical region?

Mathematics
1 answer:
Alexxandr [17]3 years ago
5 0

Answer:

1) a. Move farther into the tails

2) a. Decreases

Step-by-step explanation:

Hello!

1)

Let's say for example that you are making a confidence interval for the mean, using the Z-distribution:

X[bar] ± Z_{1-\alpha /2} * \frac{Sigma}{\sqrt{n} }

Leaving all other terms constant, this are the Z-values for three different confidence levels:

90% Z_{0.95}= 1.648

95% Z_{0.975}= 1.965

99% Z_{0.995}= 2.586

Semiamplitude of the interval is

d= Z_{1-\alpha /2} * \frac{Sigma}{\sqrt{n} }

Then if you increase the confidence level, the value of Z increases and so does the semiamplitude and amplitude of the interval:

↑d= ↑Z_{1-\alpha /2} * \frac{Sigma}{\sqrt{n} }

They have a direct relationship.

So if you change α: 0.05 to α: 0.01, then the confidence level 1-α increases from 0.95 to 0.99, and the boundaries move farther into the tails.

2)

The significance level of a hypothesis test is the probability of committing a Type I error.

If you decrease the level from 5% to 1%, then logically, the probability decreases.

I hope this helps!

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