Exam 12: Inference About a Population

Concert Tickets A simple random sample of 100 concert tickets was drawn from a normal population.The mean and standard deviation of the sample were $120 and $25,respectively. -{Concert Tickets Narrative} Test the hypothesis H₀: $\mu$ = 125 vs.H₁: $\mu$ $\neq$ 125 at the 10% significance level.

To test to see if the majority of the population exhibits a certain characteristic of interest,the alternative hypothesis of the test is H₁: p ____________________.

The t-distribution is used to develop a confidence interval estimate of the population mean when the population standard deviation is unknown.

Sinus Drug A company claims that 10% of the users of a certain sinus drug experience drowsiness.In clinical studies of this sinus drug,81 of the 900 subjects experienced drowsiness -{Sinus Drug Narrative} Explain how to use this confidence interval to test the hypotheses.

A random sample is drawn from a normal distribution with mean $\mu$ and variance $\sigma$ ².The random variable (n - 1)S² / $\sigma$ ² has a chi-squared probability distribution with n degrees of freedom.

When a population is small,it is necessary to include the ____________________ factor in our hypothesis tests and confidence interval estimators for p.

The t-statistic has two variables: the sample ____________________ and the sample ____________________.

Applicants' Grades The grades of a sample of 10 applicants,selected at random from a large population,are 71,86,75,63,92,70,81,59,80,and 90. -{Applicants' Grades Narrative} Compute the sample variance.

____________________ populations allow us to use the confidence interval estimate of a mean to produce a confidence interval estimate of the population total.

An investor is concerned with the risk associated with a portfolio of stocks.He draws a random sample of nine monthly returns (expressed as a percentage of the initial investment).These data follow: 2,5,-6,10,1,2,-3,0,and 7.Find a 95% confidence interval estimate of the population variance.

When the population standard deviation is unknown and the population is normal,the test statistic for testing hypotheses about $\mu$ is the ____________________-distribution with ____________________ degrees of freedom.

Energy Drink Consumption A researcher at the University of Washington medical school believes that energy drink consumption may increase heart rate.Suppose it is known that heart rate (in beats per minute)is normally distributed with an average of 70 bpm for adults.A random sample of 25 adults was selected and it was found that their average heartbeat was 73 bpm after energy drink consumption,with a standard deviation of 7 bpm. -{Energy Drink Consumption Narrative} Formulate the null and alternative hypotheses.

The statistic $( \bar { x } - \mu ) / ( s / \sqrt { n } )$ when the sampled population is normal is Student t-distributed with n degrees of freedom.

The 95% confidence interval would indicate that,for this shipment,the proportion of defective fuses is between 0 and 0.28.

The sampling distribution of $\hat { P }$ is approximately normal if the sample size is more than 30.

The lower limit of the 90% confidence interval for the population proportion p,given that n = 400 and $\hat { P }$ = 0.10,is 0.0247.

The test statistic to test hypotheses about the population variance has a chi-squared distribution with n -1 degrees of freedom when the population random variable has a(n)____________________ distribution.

Socialist Party Voters A pollster in Italy wants to challenge a claim that 5% of the registered voters in his country are Socialists;he thinks the percentage is lower than that.In a test of hypothesis,H₀: p = 0.05 vs.H₁: p < 0.05,his random sample of size 1,000 registered voters revealed that the number of Socialists was 40. -{Socialist Voters Narrative} Compute the p-value and explain how to use it to test the hypotheses.

{Single Mothers' Ages Narrative} What is the required condition of the techniques used in the previous questions? What graphical device can you use to check to see if that required condition is satisfied?

Physicians A random sample of 200 physicians shows that there are 36 of them who make at least $400,000 a year. -{Physicians Narrative} Construct a 99% confidence interval estimate of the population proportion of physicians who make at least $400,000 a year,and explain how to use it to test the hypotheses.