Problem of the Day
9.845, .1
A coffee machine dispenses coffee into paper cups. You’re supposed to get 10 ounces of coffee, but the amount varies slightly from cup to cup. Here are the amounts measured in a random sample of 20 cups. Is there evidence that the machine is shortchanging customers?(start by finding the mean/standard dev)
9.9 9.7 10.0 10.1
9.9 9.6 9.8 9.8
10.0 9.5 9.7 10.1
9.9 9.6 10.2 9.8
10.0 9.9 9.5 9.9
Problem of the Day
A researcher found that a 98% confidence interval for the mean hours per week spent studying by college students was (13, 17). Which is true?
I. There is a 98% chance that the mean hours per week spent studying by college students is between 13 and 17 hours.
II. 98% of college students study between 13 and 17 hours a week.
III. Students average between 13 and 17 hours per week studying on 98% of the weeks.
A) none B) I only C) II only D) III only E) I and III
Problem of the Day
A professor was curious about her students’ grade point averages (GPAs). She took a random sample of 15 students and found a mean GPA of 3.01 with a standard deviation of 0.534. Which of the following formulas gives a 99% confidence interval for the mean GPA of the professor’s students?
Problem of the Day
At one vehicle inspection station, 13 of 52 trucks and 11 of 88 cars failed the emissions test. Assuming these vehicles were representative of the cars and trucks in that area, what is the standard error of the difference in the percentages of all cars and trucks that are not in compliance with air quality regulations? A) 0.025 B) 0.032 C) 0.049 D) 0.070 E) 0.095
Chapter 23 Inferences about Means
t­Distribution
Assumptions for Means
Independence
Randomization
"Normal"
10%
Confidence Intervals with Means
A professor at a large university believes that students take an average of 15 credit hours per term. A random sample of 24 students in her class of 250 students reported the following number of credit hours that they were taking:
Hypothesis Testing with Means
A professor at a large university believes that students take an average of 15 credit hours per term. A random sample of 24 students in her class of 250 students reported the following number of credit hours that they were taking:
A company has set a goal of developing a battery that lasts over 5 hours (300 minutes) in continuous use. A first test of 12 of these batteries measured the following life spans (in
minutes): 321, 295, 332, 351, 281, 336, 311, 253, 270, 326, 311, and 288. Is there evidence to suggest that the company has met their goal?
Practice Problem
Hoping to lure more shoppers downtown, a city builds a new public parking garage in the central business district. The city plans to pay for the structure through parking fees. During a two­month period (44 weekdays), daily fees collected averaged $126, with a standard deviation of $15. Write a 90% confidence interval for the mean daily income this parking garage will generate. Interpret this confidence interval in context. The consultant who advised the city on this project predicted that parking revenues would average $130 per day. Do you think the consultant was correct? Practice Problem
A company with a large fleet of cars hopes to keep gasoline costs down and sets a goal of attaining a fleet average of at least 26 miles per gallon. To see if the goal is being met, they check the gasoline usage for 50 company trips chosen at random, finding a mean of 25.02 mpg and a standard deviation of 4.83 mpg. Is this strong evidence that they have failed to attain their fuel economy goal?
Practice Problem
A company with a large fleet of cars hopes to keep gasoline costs down and sets a goal of attaining a fleet average of at least 26 miles per gallon. To see if the goal is being met, they check the gasoline usage for 50 company trips chosen at random, finding a mean of 25.02 mpg and a standard deviation of 4.83 mpg. Discuss a Type I and Type II error in context.
Margin of Error
A coffee machine dispenses coffee into paper cups. You’re supposed to get 10 ounces of coffee, but the amount varies slightly from cup to cup. Here are the amounts measured in a random sample of 20 cups. What if we wanted an estimate within +/­ .05 oz with 95% confidence? How many cups should we sample?
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9.9 9.6 9.8 9.8
10.0 9.5 9.7 10.1
9.9 9.6 10.2 9.8
10.0 9.9 9.5 9.9
During an angiogram, heart problems can be examined via a small tube (a catheter) threaded into the heart from a vein in the patient’s leg. It’s important that the company that manufactures the catheter maintain a diameter of 2.00 mm. (The standard deviation is quite small.) Each day, quality control personnel make several measurements to test against at a significance level of . If they discover a problem, they will stop the manufacturing process until it is corrected. a) Is this a one­sided or two­sided test? In the context of the problem, why do you think this is important? b) Explain in this context what happens if the quality control people commit a Type I error. c) Explain in this context what happens if the quality control people commit a Type II error This chapter’s For Examples looked at mirex contamination in farmed salmon. We first found a 95% confidence interval for the mean concentration to be 0.0834 to 0.0992 parts per million. Later we rejected the null hypothesis that the mean did not exceed the EPA’s recommended safe level of 0.08 ppm based on a P­value of 0.0027. Explain how these two results are consistent. Your explanation should discuss the confidence level, the P­value, and the decision. A company claims its program will allow your computer to download movies quickly. We’ll test the free evaluation copy by downloading a movie several times, hoping to estimate the mean download time with a margin of error of only 8 minutes. We think the standard deviation of download times is about 10 minutes. How many trial downloads must we run if we want 95% confidence in our estimate with a margin of error of only 8 minutes?
Chapter 23
Readings and Examples pages 530‐552
Pgs 554‐555:1,5,7,11,13,15,25,27,35 Exit slip(on a 1/2 sheet of paper)
Some students checked 6 bags of Doritos marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.2, 28.5, 28.7, 28.9, 29.1, 29.5. Comment on the company’s stated net weight of 28.3 grams.