Step 1: State the 2 hypotheses Step 2: Select the distribution and specify the a-value. Distribution: Level of Significance: Step 3: Find the critical region. sion rule: Step 4: Calculate the test statistics. Step 5: Make a decision. Explain:
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- One study found a negative correlation between participant’s age and hours of sleep they got (as they got older, they slept less). Which additional fact would lead you to believe that the relationship between age and hours of sleep is one of causation and not correlation? Jim is 63 and sleeps more than he did when he 47. Josie is 40 and sleeps fewer hours than when she was 30. The participants were randomly selected, the sample size was large, and the participants did not know the goal of the study. Jennie sometimes has difficulty sleeping.For effective learning, an instructor advised his students to practice solving statistical problems on StatCrunch, a web-based software, at least 7 hours per week. In an in class activity, a student surveyed 15 of her 35 classmates to assess the number of hours they spend per week practicing statistics on StatCrunch. The following data was collected: 6.5, 4, 3.5, 0, 12, 5, 12, 15, 12, 0, 1, 8, 0.5, 2, 7. Is there strong evidence that the mean number of hours of StatCrunch usage in the entire class is larger than 7? Let the confidence level be 95% Find the mean Standard deviation T / z score Find the critical score Draw the normal curve with critical tscore and test statistic. Make a conclusionTo test whether actually taking Introductory Statistics decreases students’ anxieties about the field of Statistics, a 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 Do the data indicate that anxiety levels about the field of Statistics decreases after students take Introductory Statistics? Use a significance level of ? = 0.05. a) what is the test statistics and p-value? b) Find a 90% confidence interval for the difference in the anxiety levels about the field of Statistics
- Russell is doing some research before buying his first house. He is looking at two different areas of the city, and he wants to know if there is a significant difference between the mean prices of homes in the two areas. For the 39 homes he samples in the first area, the mean home price is $176,400. Public records indicate that home prices in the first area have a population standard deviation of $32,930. For the 32 homes he samples in the second area, the mean home price is $181,500. Again, public records show that home prices in the second area have a population standard deviation of $23,835. Let Population 1 be homes in the first area and Population 2 be homes in the second area. Construct a 95% confidence interval for the true difference between the mean home prices in the two areas. Round the endpoints of the interval to the nearest whole number, if necessary. Lowest Endpoint = upper Endpoint=There is actually a difference of several inches in the mean heights for the population of men and the population of women. However, a student doing a school project tries to investigate male vs. female height using a sample of each gender. By pure chance, he happens to have gotten a sample fairly tall women and a sample of fairly short men. So he wrongly concludes that there is no difference in the mean heights for men and women. What has happened? The student has made the correct decision The student has made a type I error The student has made a type II error Need more information to answerYou are interested in seeing whether emotions impact decision making. You have three groups--a happy group, a sad group, and a neutral group. For the happy group there are 5 participants and the mean risky decision making score 5.0 with a standard deviation of 0.7. For the sad group there are 5 participants and the mean risky decision making score 5.4 with a standard deviation of 1.1. For the neutral group there are 5 participants and the mean risky decision making score 5.8 with a standard deviation of 2.8. The sum of squares between samples is equal to 1.6. The sum of squares within samples is equal to 38.0. You calculated the f-ratio above. The corresponding p-value for the f-ratio you calculated is p = 0.78. Is this finding significant?
- Miranda and Karla began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Miranda took a test in Social Studies and earned a 71.4, and Karla took a test in Art History and earned a 60.9. Use the fact that all the students' test grades in the Social Studies class had a mean of 75.3 and a standard deviation of 10.7, and all the students' test grades in Art History had a mean of 66.4 and a standard deviation of 10.3 to answer the following questions.a) Calculate the z-score for Miranda's test grade.z=b) Calculate the z-score for Karla's test grade.z=c) Which person did relatively better? Miranda Karla They did equally well.If the test result is significant at 5% level, it must also be significant at 1% level. O True O FalseLogan and Brian began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Logan took a test in Art History and earned a 76.8, and Brian took a test in English and earned a 68.9. Use the fact that all the students' test grades in the Art History class had a mean of 71.9 and a standard deviation of 11.6, and all the students' test grades in English had a mean of 61 and a standard deviation of 9.4 to answer the following questions.a) Calculate the z-score for Logan's test grade.z=z= [Round your answer to two decimal places.] b) Calculate the z-score for Brian's test grade.z=z= [Round your answer to two decimal places.]c) Which person did relatively better? Logan Brian They did equally well.
- Lucille, Rocio, and Cristina are all taking College Mathematics but from different professors. They all recently took a statistics exam and the exam scores were normally distributed in each of their classes. • Lucille's class had an average grade of 78 and the standard deviation was 7. Lucille earned 83.95 on the exam. • Rocio's class had an average grade of 82 and the standard deviation was 3. Rocio earned 86.5 on the exam. • Cristina's class had an average grade of 76 and the standard deviation was 4. Cristina earmed 82.8 on the exam. Since some professors give harder exams than others, these students decided to use statistics to figure out who did the best on their exam. Use the Cumulative Z-Score Table to answer the following questions. Write your answers as a percent with two decimal places. Hint • Lucille's score places her above % of her class. • Rocio's score places her above % of her class. • Cristina's score places her above % of her class.two fifth grade classes have nearly identical mean scores on an aptitude test, but one class has a standard deviation three times that of the other. all other factors being equal, which class is easier to teach and why?The top 5 students of grade 10 section Oxygen class, James, Jessie, Jane, John, and Jack, are so eager to know their respective ranks. They keep on asking their teacher, Mr. Jacob, about who got the first rank, second, and so on. Mr. Jacob challenged them and said, "For all of you, in relation to all Grade 10 student's grades, you got the 90th percentile, 9th decile, 3rd quartile, 95th percentile, and 8th decile, respectively. Now tell me the correct rankings and prove to me that you are worth the rank you are in." Which of the following is the most probable ranking of the five students? James, John, Jack, Jessie, Jane Jane, John, Jack, Jessie, James John, Jack, James, Jessie, Jane John, James, Jessie, Jack, Jane