Let's say the population mean of high temperatures today is 64 degrees Fahrenheit with a normal distribution and a population standard deviation of 5 degrees. Does a high of 75 degrees fall in the 95% Region of Retention for high temperatures? What would you conclude about a null hypothesis that a high temperature of 75 degrees comes from this population? (Round to the nearest 4 decimal places.)

Question

BlackTom AI · Accepted Answer

Consider the population described: mean μ = 64, standard deviation σ = 5, and a normal distribution.

First, compute how far 75 is from the mean in standard deviation units: z = (75 − 64) / 5 = 11 / 5 = 2.2.

Next, compare this z-score to the 95% central region. For a normal distribution, the 95% central region corresponds to ±1.96 standard deviations from the mean. Since 2.2 standard deviations is beyond 1.96, 75 degrees lies outside the central 95% region of retention.

Consequently, the probability of observing a value as extreme as 75 (or more extreme) under the null distribution is about P(|Z| > 2.2) ≈ 2 * (1 − Φ(2.2)) ≈ 2 * (1 − 0.9861) ≈ 0.0278, which is less than the common significance level of 0.05. This yields a small p-value, indicating that such a temperature is unlikely under the assumed population distribution.

Therefore, the data provide evidence against the null hypothesis that a high temperature of 75 degrees comes from this population. The result is not consistent with the null at the 5% level, and the observed value would be considered unlikely under the assumed model.

In summary, 75 degrees falls outside the 95% retention region for this population, and the null hypothesis would be rejected at the 0.05 significance level based on this calculation.

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

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

更多留学生实用工具

智能学习助手

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