Exam 6: The Standard Deviation As a Ruler and the Normal Model

Based on data from two very large independent samples, two students tested a hypothesis about equality of population means using a = 0.05. One student used a one-tail test and rejected the null hypothesis, but the other used a two-tail test and failed to reject the null. Which of these might have been their calculated value of t?

A soft drink company is conducting research to select a new design for the can. A random sample of participants has been selected. Instead of a typical taste test with two different sodas, they actually give each participant the same soda twice. One drink is served in a predominantly red can, the other in a predominantly blue can. The order is chosen randomly. Participants are asked to rate each drink on a scale of 1 to 10. Thus, the company wishes to test if the color of the can influences the rating. The ratings were recorded for each participant. The data are shown in the table below. Does this sample indicate that there is a difference in the ratings? Test an appropriate hypothesis and state your conclusion. Rater Red Blue 1 4 6 2 7 5 3 3 6 4 8 9 5 5 2 6 9 9 7 7 10 8 5 4 9 6 8 10 9 7 11 8 8 12 3 7 13 6 5 14 8 8 15 9 10 16 7 6

Company executives wish to estimate the dollar amount that customers spend in one shopping visit to their store. Initial tests were based on a small sample but now the executives double the sample size for a follow-up test. The main purpose of the larger sample is to...

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?

The manager of a self-serve frozen yogurt shop, Purple Pear, knows that customers swirl different amounts of the creamy concoction into their cups. She samples cups from 10 costumers she believes to be representative of the customers and weighs the cups, finding a mean of 4.5 ounces and standard deviation of 0.25 ounces. Assuming these cups of frozen yogurt can be considered a random sample of all cups of frozen yogurt which of the following formulas gives a 95% Confidence interval for the mean weight of all cups of frozen yogurt?

Which of the following is true about Student's t-models? I. They are unimodal, symmetric, and bell shaped. II. They have fatter tails than the Normal model. III. As the degrees of freedom increase, the t-models look more and more like the Normal.

Textbook authors must be careful that the reading level of their book is appropriate for the target audience. Some methods of assessing reading level require estimating the average word length. We've randomly chosen 20 words from a randomly selected page in Stats: Modeling the World and counted the number of letters in each word: 5, 5, 2, 11, 1, 5, 3, 8, 5, 4, 7, 2, 9, 4, 8, 10, 4, 5, 6, 6 -For a more definitive evaluation of reading level the editor wants to estimate the text's word length to within 0.5 letters with 98% confidence. How many randomly selected words does she need to use?

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: 12 13 14 14 15 15 15 16 16 16 16 16 17 17 17 18 18 18 18 19 19 19 20 21 -Find a 95% confidence interval for the number of credit hours taken by the students in the professor's class. Interpret your interval.

Doctors at a technology research facility randomly assigned equal numbers of people to use computer keyboards in two rooms. In one room a group of people typed a manuscript using standard keyboards, while in the other room people typed the same manuscript using ergonomic keyboards to see if those people could type more words per minute. After collecting data for several days the researchers tested the hypothesis H₀: µ₁ - µ₂ = 0 against the one-tail alternative and found a P-value of 0.22. Which is true?

Do the data indicate that anxiety levels about Statistics decreases after students take AP* Statistics? Test an appropriate hypothesis and state your conclusion.

A contact lens wearer read that the producer of a new contact lens boasts that their lenses are cheaper than contact lenses from another popular company. She collected some data, then tested the null hypothesis H₀: µold - µnew = 0 against the alternative HA: µold - µnew > 0. Which of the following would be a Type II error?

Vacation days The distribution of the number of vacation days per year offered by different U.S. companies is skewed to the right. a. We collect data on the number of vacation days from a random sample of 60 companies across the United States. Why is it okay to use these data for inference even though the population is skewed? b. The mean and standard deviation of the 60 companies in our sample were 22 days and 9 days, respectively. Specify the sampling model (shape, center, spread) for the mean number of vacation days of such samples. c. Find a 95% confidence interval for the mean number of vacation days offered by U.S. companies. d. Explain what "95% confidence" means in this context.

A philosophy professor wants to find out whether the mean age of the men in his large lecture class is equal to the mean age of the women in his class. After collecting data from a random sample of his students, the professor tested the hypothesis H₀: µM - µW = 0 against the alternative HA: µM - ΜW ×0. The P-value for the test was 0.003. Which is true?

Before you took this course, you probably heard many stories about Statistics courses. Oftentimes parents of students have had bad experiences with Statistics courses and pass on their anxieties to their children. To test whether actually taking AP* Statistics decreases students' anxieties about statistics, an AP* statistics instructor gave a test to rate student anxiety at the beginning and end of his course. Anxiety levels were measured on a scale of 0-10. Here are the data for 16 randomly chosen students from a class of 180 students: Pre-course anxiety level 7 6 9 5 6 7 5 7 6 4 3 2 1 3 4 2 Post-course anxiety level 4 3 7 3 4 5 4 6 5 3 2 2 1 3 4 3 Difference (Post-Pre) -3 -3 -2 -2 -2 -2 -1 -1 -1 -1 -1 0 0 0 0 1 -Create and interpret a 90% confidence interval.