Exam 11: Introduction to Hypothesis Testing

Production Filling ​A production filling operation has a historical standard deviation of 6 ounces.When in proper adjustment,the mean filling weight for the production process is 50 ounces.A quality control inspector periodically selects at random 36 containers and uses the sample mean filling weight to see if the process is in proper adjustment. ​ ​ -{Production Filling Narrative} Using a standardized test statistic,test the hypothesis at the 5% level of significance if the sample mean filling weight is 48.6 ounces.

Toaster Oven An appliance manufacturer claims to have developed a new toaster oven that consumes an average of no more than 250 W.From previous studies,it is believed that power consumption for toaster ovens is normally distributed with a standard deviation of 18 W.A consumer group suspects the actual average is more than 250 W.They take a sample of 20 toaster ovens and calculate the average consumption to be 260 W. ​ ​ -{Toaster Oven Narrative} For a test with a level of significance of 0.05,determine the critical value.

The power of a test is the probability that a true null hypothesis will be rejected.

If the p value is less than α in a two-tail test:

Rechargeable Batteries A researcher wants to study the average lifetime of a certain brand of rechargeable batteries (in hours).In testing the hypotheses,H₀: μ = 950 hours vs.H₁: μ ≠ 950 hours,a random sample of 25 rechargeable batteries is drawn from a normal population whose standard deviation is 200 hours. ​ ​ -{Rechargeable Batteries Narrative} Recalculate β if α is lowered from 0.10 to 0.05.

A professor of linguistics refutes the claim that the average student spends 3 hours studying for the midterm exam.She thinks they spend more time than that.Which hypotheses are used to test the claim?

An alternative or research hypothesis is an assertion that holds if the null hypothesis is false.

A Type II error is represented by α; it is the probability of rejecting a true null hypothesis.

Marathon Runners A researcher wants to study the average miles run per day for marathon runners.In testing the hypotheses: H₀: μ = 25 miles vs.H₁: μ ≠ 25 miles,a random sample of 36 marathon runners drawn from a normal population whose standard deviation is 10,produced a mean of 22.8 miles weekly. ​ ​ -{Marathon Runners Narrative} Develop a 95% confidence interval estimate of the population mean.

Probabilities for Type I and Type II errors are actually ____________________ probabilities.

If a researcher fails to reject a false null hypothesis he has made a(n)____________________ error.

For a two-tail test,the null hypothesis will be rejected at the 0.05 level of significance if the value of the standardized test statistic z is:

Researchers claim that 40 tissues is the average number of tissues a person uses during the course of a cold.The company who makes Puffs brand tissues thinks that fewer of their tissues are needed.What are their null and alternative hypotheses?

For a given sample size n,if the level of significance α is decreased,the power of the test will:

In testing the hypotheses H₀: μ = 75 vs.H₁: μ < 75,if the value of the test statistic z equals −2.42,then the p-value is:

If a marketer wishes to determine whether there is evidence that average family income in a community exceeds $32,000:

As the alternative value of μ increases,so does the power of the test.

One way of expressing how well a test performs is to report its power--the probability of detecting a false null hypothesis.

The p-value of a test is the probability of observing a test statistic at least as extreme as the one computed given that the null hypothesis is true.

A Type II error is committed if we make: