7. In a given hypothesis test, the null hypothesis cannot be rejected at the 0.0

Question

7. In a given hypothesis test, the null hypothesis cannot be rejected at the 0.025 and 0.01 level, but can be rejected at the 0.0S and 0.10 levels. The most accurate statement we can make about the value for this test is: 8. A personnel manager reads in a national newspaper that the average office worker wastes 4.5 hours per week by arriving late, socializing, conduct personal business, working slow, faking illness, taking long lunch hours, and sleeping on the job. By observing his office staff, he obtains a random sample for a hypothesis test because he believes that his staff is different. The average time wasted per week for 10 weeks was 4.1 hours with a standard deviation of 1.33 hours. If a hypothesis test was performed at the 0.01 level with an assumption of a normally distributed population, the test statistic and p-values are: THE NEXTTWO QUESTIONS (9-10 ARE TOGETHER A state transportation official claims that the mean waiting time at exit booths from a toll road near the capitol is at least 0.40 minutes. Historically, the standard deviation (a) of waiting time has been 0.16 minutes. For a sample of 135 motorists exiting the toll road, it was found that the mean waiting time was X -0.381 minutes. At the 0.025 level of significance, is there sufficient evidence to reject the official's claim? 9. If the null hypothesis were true, the probability of obtaining a sample mean as large, or larger, than the one found in the test is (i.e., p-value)? H 0.373 minutes, then the probability of correctly If the mean waiting time were actually rejecting the null hypothesis would equal 10. Hint: Reject He if X

Explanation / Answer

Solution:-

8. State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: = 4.5
Alternative hypothesis: 4.5
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), and the z - statistic (z).
SE = s / sqrt(n)
S.E = 1.33/ = = 0.421
z = (x - ) / SE
z = - 0.95
Where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.
Since we have a two-tailed test, the P-value is the probability less than -0.95 or greater than 0.95
The P-Value is 0.3421
Interpret results. Since the P-value (0.3421) is greater than the significance level (0.01), we cannot reject the null hypothesis.

Related Questions

Navigate

• Browse (All)
• Browse 7
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.