Confidence Intervals Practice Questions and Solutions

11/16/23, 2:59 PM ccs.casa.uh.edu/cgi-bin/canvas?course=2122_student_f6dc91c4765a0657075c3139164d2a78930bc858b2ca81f953e01623236… https://ccs.casa.uh.edu/cgi-bin/canvas?course=2122_student_f6dc91c4765a0657075c3139164d2a78930bc858b2ca81f953e016232362fb11&mode=… 1/8 wait=-1008040, due=1698555540, due2=0 Question number 1. Your answer was A. Correct. As the length of the confidence interval for the population mean decreases, the degree of confidence in the interval's actually containing the population mean A decreases B does not change C increases Question number 2. Your answer was B. Correct. The gas mileage for a certain model of car is known to have a standard deviation of 4 mi/gallon. A simple random sample of 81 cars of this model is chosen and found to have a mean gas mileage of 28.4 mi/gallon. Construct a 97% confidence interval for the mean gas mileage for this car model. A (20.876, 35.924) B (27.436, 29.364) C (28.293, 28.507) D (19.720, 37.080) E (27.564, 29.236) F None of the above

11/16/23, 2:59 PM ccs.casa.uh.edu/cgi-bin/canvas?course=2122_student_f6dc91c4765a0657075c3139164d2a78930bc858b2ca81f953e01623236… https://ccs.casa.uh.edu/cgi-bin/canvas?course=2122_student_f6dc91c4765a0657075c3139164d2a78930bc858b2ca81f953e016232362fb11&mode=… 2/8 Question number 3. Your answer was B. Correct. What will reduce the width of a confidence interval? A Decrease number in sample. B Increase number in sample. C Increase variance. D Increase confidence level. Question number 4. Your answer was E. Correct. If the 90% confidence limits for the population mean are 34 and 46, which of the following could be the 99% confidence limits A (38, 45) B (39, 43) C (39, 41) D (36, 41) E (30, 50)

11/16/23, 2:59 PM ccs.casa.uh.edu/cgi-bin/canvas?course=2122_student_f6dc91c4765a0657075c3139164d2a78930bc858b2ca81f953e01623236… https://ccs.casa.uh.edu/cgi-bin/canvas?course=2122_student_f6dc91c4765a0657075c3139164d2a78930bc858b2ca81f953e016232362fb11&mode=… 3/8 F None of the above Question number 5. Your answer was A. Correct. A 99% confidence interval for the mean of a population is to be constructed and must be accurate to within 0.3 unit. A preliminary sample standard deviation is 2.3. The smallest sample size n that provides the desired accuracy is A 390 B 378 C 387 D 402 E 399 F None of the above Question number 6. Your answer was A. Correct. An SRS of 22 students at UH gave an average height of 5.6 feet and a standard deviation of .1 feet. Construct a 90% confidence interval for the mean height of students at UH. A (5.563, 5.637)

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11/16/23, 2:59 PM ccs.casa.uh.edu/cgi-bin/canvas?course=2122_student_f6dc91c4765a0657075c3139164d2a78930bc858b2ca81f953e01623236… https://ccs.casa.uh.edu/cgi-bin/canvas?course=2122_student_f6dc91c4765a0657075c3139164d2a78930bc858b2ca81f953e016232362fb11&mode=… 4/8 B (5.428, 5.772) C (4.100, 7.400) D (4.350, 7.050) E (5.592, 5.608) F None of the above Question number 7. Your answer was B. Correct. Which test statistic should be used when computing a confidence interval given only the number in a sample, the population standard deviation and sample mean? A q B z C p D t Question number 8. Your answer was B. Correct. An important problem in industry is shipment damage. A windshield factory ships its product by truck and determines that it cannot meet its profit expectations if, on average, the number of damaged items per truckload is greater than 12. A random sample of 12 departing truckloads is selected at the delivery point and the average number of damaged items per truckload is calculated to be 11.3 with a calculated sample of variance of 0.49. Select a 99% confidence interval for the true mean of damaged items.

11/16/23, 2:59 PM ccs.casa.uh.edu/cgi-bin/canvas?course=2122_student_f6dc91c4765a0657075c3139164d2a78930bc858b2ca81f953e01623236… https://ccs.casa.uh.edu/cgi-bin/canvas?course=2122_student_f6dc91c4765a0657075c3139164d2a78930bc858b2ca81f953e016232362fb11&mode=… 5/8 A (11.37, 12.63) B (10.67, 11.93) C (10.69, 11.91) D (-0.6285, 0.6285) E (48.26, -30.02) F None of the above Question number 9. Your answer was D. Correct. The amounts (in ounces) of juice in eight randomly selected juice bottles are: 15.8, 15.6, 15.1, 15.2, 15.1, 15.5, 15.9, 15.5 Construct a % confidence interval for the mean amount of juice in all such bottles. Assume an approximate Normal distribution. A (15.329, 15.596) B (15.316, 15.609) C (15.289, 15.636) D (15.264, 15.661) E None of the above

11/16/23, 2:59 PM ccs.casa.uh.edu/cgi-bin/canvas?course=2122_student_f6dc91c4765a0657075c3139164d2a78930bc858b2ca81f953e01623236… https://ccs.casa.uh.edu/cgi-bin/canvas?course=2122_student_f6dc91c4765a0657075c3139164d2a78930bc858b2ca81f953e016232362fb11&mode=… 6/8 Question number 10. Your answer was D. Correct. Among 20 golden hamster litters recorded, there was a sample mean of baby hamsters, with a sample standard deviation of hamsters per liter. Create a % confidence interval for the mean number of baby hamsters per liter. A B C D E F None of the above Question number 11. Your answer was D. Correct. Which of the following is not appropriate to use the z-confidence interval for . A The sample size is greater than 30. B The variable has a Normal distribution. C The sample is based on a simple random sample (SRS).

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11/16/23, 2:59 PM ccs.casa.uh.edu/cgi-bin/canvas?course=2122_student_f6dc91c4765a0657075c3139164d2a78930bc858b2ca81f953e01623236… https://ccs.casa.uh.edu/cgi-bin/canvas?course=2122_student_f6dc91c4765a0657075c3139164d2a78930bc858b2ca81f953e016232362fb11&mode=… 7/8 D The population standard deviation, , is unknown. E All of the above are appropriate. Question number 12. Your answer was A. Correct. A 90% confidence interval for a population parameter means that if a large number of confidence intervals were constructed from repeated samples, then on average, 90% of these intervals would contain the true parameter. A True B False Question number 13. Your answer was B. Correct. Suppose you were told that a 99% confidence interval for the population mean of mpg of a hybrid car was (27, 35). Determine the point estimate for this population mean. A 2.58 B C D E

11/16/23, 2:59 PM ccs.casa.uh.edu/cgi-bin/canvas?course=2122_student_f6dc91c4765a0657075c3139164d2a78930bc858b2ca81f953e01623236… https://ccs.casa.uh.edu/cgi-bin/canvas?course=2122_student_f6dc91c4765a0657075c3139164d2a78930bc858b2ca81f953e016232362fb11&mode=… 8/8 F None of the above. Question number 14. Your answer was A. Correct. Which of the following statements are true? A The sample mean is an unbiased estimate of the population mean. B The t-critical value is an estimate of the population standard deviation. C The sample standard deviation is an unbiased estimate of the population standard deviation. D The z-critical value is an estimate of the population mean. E None of the above.

quiz 9

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