Exam 11: Introduction to Hypothesis Testing

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} What can we conclude at the 5% significance level regarding the null hypothesis?

The probability of a test statistic falling in the rejection region is equal to the value of ____________________.

After you set up the hypotheses and collect your data,you calculate the statistic that serves as the criterion for making your decision.This number is called the ____________________ statistic.

Which of the following is an appropriate null hypothesis?

LSAT Scores The Admissions officer for the graduate programs at the University of Pennsylvania believes that the average score on the LSAT exam at his university is significantly higher than the national average of 1,300.An accepted standard deviation for LSAT scores is 125.A random sample of 25 scores had an average of 1,375. ​ ​ -{LSAT Scores Narrative} State the appropriate null and alternative hypotheses.

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} Develop a 95% confidence interval and use it to test the hypothesis.

Watching the News A researcher claims viewers spend an average of 40 minutes per day watching the news.You think the average is higher than that.In testing your hypotheses H₀: μ = 40 vs.H₁: μ > 40,the following information came from your random sample of viewers: = 42 minutes,n = 25.Assume σ = 5.5,and α = 0.10. ​ ​ -{Watching the News Narrative} Determine the p-value.

Suppose that 9 observations are drawn from a normal population whose standard deviation is 2.The observations are: 15,9,13,11,8,12,11,7,and 10.At 95% confidence,you want to determine whether the mean of the population from which this sample was taken is significantly different from 10. a.State the null and alternative hypotheses. b.Compute the value of the test statistic. c.Compute the p-value. d.Interpret the results.

A spouse suspects that the average amount of money spent on Christmas gifts for immediate family members is above $1,200.The correct set of hypotheses is:

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 n is increased from 25 to 40.

For a given sample size,the probability of committing a Type II error will increase when the probability of committing a Type I error is reduced.

The p-value of a test is the:

If we reject the null hypothesis when it is false,then we have committed:

If we reject the null hypothesis,we conclude that there is enough statistical evidence to infer that the alternative hypothesis is true.

To calculate the probability of a(n)____________________ error you need to specify a value of μ other than the one given in the null hypothesis.

The operating characteristic curve plots the values of β (the probability of committing a Type II error)versus the values of the population mean μ.

To test the hypotheses: H₀: μ = 40 vs.H₁: μ ≠ 40,we draw a random sample of size 16 from a normal population whose standard deviation is 5.If we set α = 0.01,find the probability of committing a Type II error when μ = 37.

If we reject the null hypothesis,we conclude that:

Watching the News A researcher claims viewers spend an average of 40 minutes per day watching the news.You think the average is higher than that.In testing your hypotheses H₀: μ = 40 vs.H₁: μ > 40,the following information came from your random sample of viewers: = 42 minutes,n = 25.Assume σ = 5.5,and α = 0.10. ​ ​ -{Watching the News Narrative} Calculate the value of the test statistic.

LSAT Scores The Admissions officer for the graduate programs at the University of Pennsylvania believes that the average score on the LSAT exam at his university is significantly higher than the national average of 1,300.An accepted standard deviation for LSAT scores is 125.A random sample of 25 scores had an average of 1,375. ​ ​ -{LSAT Scores Narrative} Calculate the p-value.