For a two-tailed hypothesis test with a test statistic value of z = 2.09, the p-value is _____.

Question

For a two-tailed hypothesis test with a test statistic value of z = 2.09, the p-value is   _____.

BlackTom AI · Accepted Answer

Question restatement: For a two-tailed hypothesis test with a test statistic value of z = 2.09, the p-value is _____.

Option A: .0404
- Interpretation: This value is close to 0.04, which would correspond to a p-value around 4%.
- Why this is not correct: A z-score of 2.09 corresponds to a tail area of about 0.009 on one side (since 2.09 is beyond the 0.975 quantile but not far beyond). Doubling that tail area for a two-tailed test gives roughly 0.018, which is notably smaller than 0.0404. The mismatch suggests this option overestimates the two-tailed p-value for z = 2.09.

Option B: .0202
- Interpretation: This value is around 2.0%, which would be half of the approximate two-tailed p-value for a z around 2.09.
- Why this is not correct: For a two-tailed p-value, you should take the full combined tail area on both sides. Since the one-tail area is near 0.009, doubling it should yield around 0.018, not 0.0202. The discrepancy arises from the precise tail area calculation, but this option is slightly lower than the expected two-tailed value for z = 2.09.

Option C: .0366
- Interpretation: This value is about 3.66%, which aligns with a two-tailed p-value calculation for a z-score slightly above 2.0.
- Why this is plausible: Using a standard normal table or calculator, Phi(2.09) ≈ 0.9817. The one-tail area is 1 − 0.9817 ≈ 0.0183. Doubling gives 0.0366. This matches the standard two-tailed p-value computation for z = 2.09.

Option D: .4899
- Interpretation: This value is around 0.49, i.e., nearly 50%, which would indicate an almost non-informative test result.
- Why this is not correct: A z-value of 2.09 lies far into the tail; such a large p-value would imply the observed statistic is highly compatible with the null, which is inconsistent with the observed z exceeding 2 standard deviations. This option grossly overstates the p-value and is not consistent with the standard normal distribution tail areas.

Synthesis: To determine the p-value for a two-tailed z-test, compute the one-tail probability P(Z > 2.09) and double it. Using the standard normal distribution, P(Z > 2.09) ≈ 0.0183, and doubling yields approximately 0.0366. Therefore, the option that corresponds to this calculation is the one that matches 0.0366, while the others misestimate the tail areas for this z-score.

MGS2150W07 final- Requires Respondus LockDown Browser

For a two-tailed hypothesis test with a test statistic value of z = 2.09, the p-value is _____.

查看解析

登录即可查看完整答案

类似问题

Which one is true?

For an upper-tail hypotheses about a population mean with σ known and α=5%, which one is the rejection region?

For a given sample, the P-value for upper tail test is x, and the P-value for two-tailed test is y, then

For a sample size of 30, changing from using the t distribution to using the standard normal distribution in a hypothesis test _____.

Exhibit 9-5 n = 16 H0: μ ≥ 80 = 75.607 Ha: μ < 80 σ = 8.6 Assume the population is normally distributed. Refer to Exhibit 9-5. The p-value is equal to _____.

Exhibit 9-1 Refer to Exhibit 9-1. If the test is done at a .01 level of significance, the null hypothesis should _____.

What conclusion for a test would correctly detect a difference between the actual parameter and the hypothesized value for the parameter? c08.p089.q0008

Which of the following statements descrbes best the characteristics of the one-tailed and two-tailed tests in statistical hypothesis testing?

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单

MGS*2150*W07 final- Requires Respondus LockDown Browser

For a two-tailed hypothesis test with a test statistic value of z = 2.09, the p-value is _____.

查看解析

登录即可查看完整答案

类似问题

Which one is true?

For an upper-tail hypotheses about a population mean with σ known and α=5%, which one is the rejection region?

For a given sample, the P-value for upper tail test is x, and the P-value for two-tailed test is y, then

For a sample size of 30, changing from using the t distribution to using the standard normal distribution in a hypothesis test _____.

Exhibit 9-5 n = 16 H0: μ ≥ 80 = 75.607 Ha: μ < 80 σ = 8.6 Assume the population is normally distributed. Refer to Exhibit 9-5. The p-value is equal to _____.

Exhibit 9-1 ​ ​ Refer to Exhibit 9-1. If the test is done at a .01 level of significance, the null hypothesis should _____.

What conclusion for a test would correctly detect a difference between the actual parameter and the hypothesized value for the parameter? c08.p089.q0008

Which of the following statements descrbes best the characteristics of the one-tailed and two-tailed tests in statistical hypothesis testing?

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单

MGS2150W07 final- Requires Respondus LockDown Browser

Exhibit 9-1 Refer to Exhibit 9-1. If the test is done at a .01 level of significance, the null hypothesis should _____.