Question

question 5
1 pts
for an upper - tailed hypothesis test, you want to be 98% confident that you dont make a type i error, and the test - statistic is 1.83. what is your conclusion using the p - value approach?

• p - value = 0.0336 > 0.02, so do not reject (h_0)
• p - value = 0.0336 ≤ 0.98, so reject (h_0)
• p - value = 0.0336 ≤ 0.98, so do not reject (h_0)
• p - value = 0.9664 ≤ 0.98, so reject (h_0)
• p - value = 0.9664 ≤ 0.98, so do not reject (h_0)
• p - value = 0.9664 > 0.02, so do not reject (h_0)
• p - value = 0.9664 > 0.02, so reject (h_0)
• p - value = 0.0336 > 0.02, so reject (h_0)

question 6
1 pts
for a two - tailed z - test with (alpha = 0.03) and a test statistic of - 2.02, what is your conclusion using the critical value approach?

• (z_{alpha}=pm1.88), so do not reject the null hypothesis
• p - value = 0.0217, so do not reject the null hypothesis
• (z_{alpha/2}=pm2.17), so reject the null hypothesis
• p - value = 0.0434, so reject the null hypothesis
• (z_{alpha/2}=pm2.17), so do not reject the null hypothesis
• p - value = 0.0434, so do not reject the null hypothesis
• p - value = 0.0217, so reject the null hypothesis
• (z_{alpha}=pm1.88), so reject the null hypothesis

question 7
1 pts

Explanation:

Question 5

Step1: Determine significance level

For 98% confidence (not making Type I error), $\alpha = 1 - 0.98 = 0.02$.

Step2: Find p - value for upper - tailed test

Test statistic $z = 1.83$. For upper - tailed, $p - value=P(Z > 1.83)=1 - P(Z\leq1.83)$. From standard normal table, $P(Z\leq1.83)=0.9664$, so $p - value = 1 - 0.9664 = 0.0336$.

Step3: Compare p - value and $\alpha$

We have $p - value = 0.0336$ and $\alpha = 0.02$. Since $0.0336>0.02$, we do not reject $H_0$.

Step1: Determine critical value for two - tailed test

For $\alpha = 0.03$, two - tailed, so $\alpha/2=0.015$. The critical values are $z_{\alpha/2}=\pm z_{0.015}$. From standard normal table, $z_{0.015}=2.17$ (since $P(Z > 2.17)=0.015$), so $z_{\alpha/2}=\pm2.17$.

Step2: Compare test statistic and critical values

Test statistic $z=-2.02$. The critical values are $\pm2.17$. Since $-2.17 < - 2.02<2.17$, we do not reject the null hypothesis.

Answer:

p - value = 0.0336 > 0.02, so do not reject $H_0$

Question 6