Stat3360.001 - Spring 2017 Homework7: GK Ch.12, YK Ch.9 Due: April 3 Name (First, Last):______________________________________________________ NetID: ______________________________ 1- 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. We want to test their claim and find out whether the actual percentage is not 10%. a. Is there enough evidence at the 5% significance level to infer that the competitor is correct? = ________ H0 : ____________ H1 : ____________ z = ________ p-value = _______ Conclusion: b. Construct a 95% confidence interval estimate of the population proportion of the users of this allergy drug who experience drowsiness. = ________ z/2= ________ LCL=_________ UCL=________ Conclusion: 2- A random sample of 200 physicians shows that there are 36 of them who make at least $400,000 a year. a. Can we conclude at the 5% significance level that the true proportion of physicians in the population who make at least $400,000 a year is less than 0.24? = ________ H0 : ____________ H1 : ____________ z = ________ p-value = _______ Conclusion: Stat3360.001 - Spring 2017 Homework7: GK Ch.12, YK Ch.9 Due: April 3 b. Construct a 99% confidence interval estimate of the population proportion of physicians who make at least $400,000 a year. = ________ z/2= ________ LCL=_________ UCL=________ Conclusion: 3- A major electronics store chain is interested in estimating the average amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: = $50.50 and s2 = 400. Find the 95% confidence interval for the average amount the credit card customers spent on their first visit to the chain's new store in the mall. =__________ t/2, = ________ LCL=_________ UCL=________ Conclusion: 4- A random sample of 10 single mothers was drawn from a Obstetrics Clinic. Their ages are 22, 17, 27, 20, 23, 19, 24, 18, 19, and 24 years. a. Estimate the population mean with 90% confidence. (you may used the table provided to assist your calculations of s2) x Sum(x)= x2 Sum(x2)= =__________ s2=_______________ s=__________ =__________ t/2, = ________ LCL=_________ UCL=________ Conclusion: Stat3360.001 - Spring 2017 Homework7: GK Ch.12, YK Ch.9 Due: April 3 b. Test to determine if we can infer at the 5% significance level that the population mean is not equal to 20. = ________ H0 : ____________ H1 : ____________ t = _____________ p-value = _______ Conclusion: 5- The air pumps at service stations come equipped with a gauge to regulate the air pressure of tires. A mechanic believes that the gauges are in error by at least 3 pounds per square inch. To test his belief he takes a random example of 50 air pump gauges and determines the difference between the true pressure (as measured by an accurate measuring device) and the pressure shown on the air pump gauge. The mean and the standard deviation of the sample are = 3.4 and s = 1.2. Can the mechanic infer that he is correct at the 5% significance level? Assume tire pressures have a normal distribution. = ________ H0 : ____________ H1 : ____________ t = _____________ p-value = _______ Conclusion: Stat3360.001 - Spring 2017 Homework7: GK Ch.12, YK Ch.9 Due: April 3 6- 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. (You may use the table provided to assist your calculation of s2). x Sum(x)= x2 Sum(x2)= =__________ s2=_______________ =_________ 2/2, = ________ 21-/2, = ________ LCL=_________ UCL=________ Conclusion: 7- The sales manager of a large multinational corporation is concerned that some salespersons perform very well and others quite poorly. To help analyze the problem he draws a random sample of 20 salespersons, determines their commission incomes (in thousands of dollars), and calculates the following statistics: = $37.2, and s = $7.8. Do these statistics provide sufficient evidence at the 5% significance level to conclude that the population variance exceeds $35 million2? =_________ H0 : ____________ H1 : ____________ 2 = ____________ p-value = _______ Conclusion: Grade: _________