Assignment 6 Fa 2023

Name POLS 3316. Quantitative Methods Dr. Scott Basinger Homework Assignment #6 Distributed Thursday, October 19, 2023 Due Thursday, October 26, 2023 1. A highway patrol car is positioned at a randomly selected interstate milepost where the speed limit is 65 mph. A random sample of 25 cars reveals an average speed of 67.7 mph, with a standard deviation of 6.0 miles per hour. A 95% confidence interval for the average car’s speed on the interstate is from ________ to ________ mph. Standard Error of 𝑥𝑥̅ t * Critical Value Margin of Error 2. The retention region for the null hypothesis that the average car drives 65 mph is from _______ to _______ mph. t statistic 3. Calculate the t statistic against the null hypothesis µ 0 = 65.0. Based on this sample of drivers, the highway patrol officer should ________ the null hypothesis that the average car’s speed is 65 mph. 4. A random sample of 20 first-grade elementary students was administered the Stanford-Binet intelligence test. The sample yielded a mean mental age of 6.25 years with a standard deviation of 0.9 years. A 95% confidence interval for the average first-grade student’s mental age is from _______ to _______ years. Standard Error of 𝑥𝑥̅ t * Critical Value Margin of Error 5. The retention region for the null hypothesis that the average first-grader has a mental age of 6.0 years is from _______ to _______ years. t statistic 6. Calculate the t statistic against the null hypothesis µ 0 = 6.0. Based on this sample, the school should ________ the null hypothesis that the average first-grader has mental age of 6.0 years old.

Name 7. A retailer selected ten quartz watches and set them to the identical time. After four weeks, the times shown on these watches were compared to the atomic clock . The ten watches gained the following amounts of time, in seconds: –3 +7 +2 +6 +8 +2 –3 +6 +11 +8 The average number of seconds gained from this sample of watches equals 𝒙𝒙 � = ________ seconds. 8. Fill in the table below! The standard deviation of seconds gained from this sample equals s = ________ . Values 𝑥𝑥 𝑖𝑖 Deviations from Mean ( 𝑥𝑥 𝑖𝑖 − 𝑥𝑥̅ ) Squared Deviations from Mean ( 𝑥𝑥 𝑖𝑖 − 𝑥𝑥̅ ) 2 –3 +7 +2 +6 +8 +2 –3 +6 +11 +8 Sum ( ∑ ∎ ) Average ( ∑ ∎ ) 𝑁𝑁 𝑥𝑥̅ = Variance ( ∑ ∎ ) 𝑁𝑁−1 s 2 = 9. A 95% confidence interval for the mean time gained by this model of watch is from ________ to ________ seconds. Standard Error of 𝑥𝑥̅ t * Critical Value Margin of Error 10. If the watches are truly accurate, they should gain or lose 0 seconds on average. The retention region for the null hypothesis of ± 0 seconds (gained or lost) is from ________ to ________ seconds. t statistic 11. Calculate the t statistic against the null hypothesis µ 0 = 0.0. Based on this sample, the retailer should ________ the null hypothesis that this brand of watch is accurate.