In the last chapter we considered parameter estimation andconfidence intervals. We now look at the other primary aspect ofinferential statistics, hypothesis testing.
In statistics, a hypothesis is a claim or statement about aparameter of a population.
Often the hypothesis will have to do with the values of parameters.
Rare Event Rule for Inferential Statistics
We make inferences using the Rare Event Rule.
If, under a given assumption, the probability of a particularobserved event is extremely small, we conclude that the assumptionis probably not correct.
We now consider the components of a formal hypothesis test.
The null hypothesis contains equality and the alternative oftencontains the claim.
We will use a concept known as the p-value. The p-value is theprobability of getting a value of the test statistic that is at least asextreme as the one obtained from the sample data.
Critical Region, Significance Level, andCritical Value
The region may be two-tailed, left-tailed, or right-tailed
1. Reject the null hypothesis. 2. Fail to reject the null hypothesis.
• Type I error: Reject H0 when it is true. • Type II error: Fail to reject H0 when it is false.
We denote the probability of a type I error with α and a type IIerror with β.
2. Determine significance level, often α = .05
3. Calculate test statistic and p−value4. Conclusion: Reject or Fail to Reject and Interpretation
A simple random sample of 40 adult males yielded the followingresults: x = 172.55 and s = 26.33. Use a significance level of 0.05to test the claim that men have a mean weight greater than 166.3 lb.
A sample of 40 uninterruptible power supplies yielded the followingresults: x = 123.59 volts and s = 0.31 volts. Use a significancelevel of 0.05 to test the manufacturers claim that the mean voltageis equal to 120 volts.
A company that produces cell phone batteries claims their batterieslast at least 35 hours. Use a significance level of 0.05 to test theclaim. The data collected is listed below.
In a survey, 1864 out of 2246 randomly selected adults said textingwhile driving should be illegal. Use a significance level of 0.05 totest the claim that more than 80% of adults believe texting shouldbe illegal while driving.
Clinical trials involved treating patients with Tamiflu. Among 724patients treated, 72 experienced nausea as an adverse reaction. Usea significance level of 0.05 to test the claim that the rate of nauseais greater than the 6% rate experienced by patients given a placebo. Does nausea appear to be a concern for those given the Tamiflutreatment.
In a survey of 703 randomly selected workers, 61% got their jobsthrough networking. Use a significance level of 0.05 to test theclaim that most (more than 50%) workers got their jobs throughnetworking. What does the result suggest about the strategy forfinding a job after graduation?
2009–10 Health Update and Permission to Give Over-The-Counter Medication Please complete a separate form for each student and return it to the School in an envelope marked “School Nurse” by August 1, 2009. Please attach an updated immunization record. This mandatory form must be completed and signed by a parent and on file in the clinic prior to the administration of over-the-count
In the last chapter we considered parameter estimation andconfidence intervals. We now look at the other primary aspect ofinferential statistics, hypothesis testing.
We will use a concept known as the p-value. The p-value is theprobability of getting a value of the test statistic that is at least asextreme as the one obtained from the sample data.
A simple random sample of 40 adult males yielded the followingresults: x = 172.55 and s = 26.33. Use a significance level of 0.05to test the claim that men have a mean weight greater than 166.3 lb.
A sample of 40 uninterruptible power supplies yielded the followingresults: x = 123.59 volts and s = 0.31 volts. Use a significancelevel of 0.05 to test the manufacturers claim that the mean voltageis equal to 120 volts.