4/17/2016 Stats 250 W16 HW 10 Closing date: 4/18/16 5:00PM Last Saved: 4/17/16 8:44PM 57142d318bea840b00fac568 Question 1 : 1 point(s) What are Expected Counts? A chi-square test involves a set of counts called \"expected counts.\" What are the expected counts? Question 1 Multiple Choice Options [X] Hypothetical counts that would occur if the null hypothesis were true. Hypothetical counts that would occur if the alternative hypothesis were true The actual counts that did occur in the study. Question 2 Background : Blood Type According to the American Association of Hematology, the proportion of blood phenotypes for A, B, AB, and O in the population of all U.S. adults are 0.41, 0.10, 0.04, and 0.45, respectively. A researcher at Penn State's Medical Center is interested in assessing whether the distribution for blood phenotypes for Penn State's undergraduate student body matches these U.S. rates. From Penn State's medical database, 200 undergraduates are randomly chosen resulting in 89 that are of Type A, 18 of Type B, 12 of Type AB, and the remaining 81 of Type O. The Goodness of Fit hypotheses to be tested using the above results are versus Ha: at least one probability is not as listed in H0; where is the proportion of all Penn State's undergraduates that are of Type A, is the proportion of all Penn State's undergraduates that are of Type B, and so on. Question 2 Subquestions 2.a 0 point(s) If the null hypothesis is true, how many students in the random sample would be expected to fall in the Type A category? 25 1/11 4/17/2016 41 82 2.b 1 point(s) The researcher conducting the test obtained an observed test statistic value of 3.7. Which of the following must be the corresponding p-value? 0.696 0.296 0.196 0.039 0.003 2.c 2 point(s) The observed test statistic of 3.7 is above the expected value for such a test statistic if the null hypothesis were true. About how many standard deviations above the expected value is it? 0.29 0.7 2.45 3 Question 3 Background : Handedness and Eye Preference A researcher would like to see if there is an association between handedness and eye preference. A random sample of 150 adult participants was selected. For each participant, the researcher determined two things: 1) whether the person is left-handed or right-handed; and 2) which eye the person prefers to use when looking through a camera viewfinder. The results are shown in the table. 2/11 4/17/2016 Question 3 Subquestions 3.a 0 point(s) The researcher is interested in assessing if there is an association between handedness and eye preference for the population of all such adults. The data were entered into R and the some results were obtained. What is the name of the statistical test being performed by the researcher? Goodness of Fit Test of Homogeneity Test of Independence 3.b 1 point(s) If there is no association between handedness and eye preference, what is the expected number of lefthanded adults who prefer to use their right eye when looking through a camera viewfinder? 5 13 13.33 20 25 30 3.c 2 point(s) The R output provides the results of the chi-square test. 3/11 4/17/2016 Does there appear to be a statistically significant association between handedness and eye preference for the population of all such adults? (Use a 5% significance level, select your answer, think about the reasoning behind your answer.) Yes No Question 4 Background : Good Sleep or Bad Sleep? A study was conducted to identify the factors affecting quality of sleep for university students. A survey of 290 university students of different majors aged 17-29 years old revealed that 67.2% of these students suffered from poor sleep and 32.8% had good sleep quality. Further analyses were conducted to assess if the distribution of sleep quality was same for the various age groups of Young (19 years or younger), Middle (over 19 years but less than 24 years old), and Old (24 years or older). The following data shows the sleep quality results for each age group. Question 4 Subquestions 4.a 0 point(s) Select the name of the test that should be used to assess if the distribution of the response is the same for the population of men and the population of women. Goodness of Fit Test of Homogeneity Test of Independence 4/11 4/17/2016 4.b 1 point(s) If the distribution of the sleep quality is the same for the three age populations of university students, what is the expected value of the test statistic? 0 1 2 3 4.c 2 point(s) If the distribution of the sleep quality is the same for the three age populations of university students, how many young students would you expect to have good sleep? 25 25.22 26 77 95 4.d 2 point(s) The observed chi-square test statistic value was computed to be 4.73. Look up the appropriate bounds for the p-value to help you select the appropriate word(s) needed to complete this conclusion. At a 5% significance level, it appears that the distribution of sleep quality ____the same for the three age group populations of university students. Is Is not Question 5 Background : Personality and Attitude 5/11 4/17/2016 A survey of a random sample of 100 adults was taken and their personality type (A or B) and their attitude toward small cars (positive, neutral, negative) were recorded. The data are summarized in the table shown. Question 5 Subquestions 5.a 0 point(s) The researcher is interested in assessing if there is a relationship between personality type and their attitude toward small cars for the population of all such adults. What is the name of the statistical test being performed by the researcher? Goodness of Fit Test of Homogeneity Test of Independence 5.b 1 point(s) If there is no relationship between personality type and their attitude toward small cars for the population of all such adults, how many Type A adults would you have expected to have a positive attitude toward small cars? 0 2 22 22.2 23 25 37 60 5.c 6/11 4/17/2016 2 point(s) The data were entered into R and part of the output is provided. Valuedf P-value Pearson Chi-Square1.405 2 0.495 If there is no relationship between personality type and their attitude toward small cars for the population of all such adults, what is the expected value of the test statistic? 0 0.495 1.405 2 5.d 2 point(s) Does there appear to be a statistically significant relationship between personality type and their attitude toward small cars for the population of all such adults? Use a 5% significance level, select your answer, and think about the reasoning behind your answer. Yes No Question 6 : 1 point(s) What does the p-value tell us? A researcher was conducting a chi-square test of homogeneity to assess if the distribution of voter preference is the same across four different districts. Analyzing the results led to a p-value of 0.03. Which statement(s) are correct regarding this p-value? Select all that apply. Question 6 Multiple Choice Options The probability that the null hypothesis is true is 0.03. The probability that the alternative hypothesis is true is 0.03. The smallest level of significance at which the null hypothesis can be rejected is 0.03. The largest level of significance at which the null hypothesis can be rejected is 0.03. 7/11 4/17/2016 Question 7 Background : Name That Scenario: Polling Organization One important aspect in statistics is to understand which statistical methods or procedures are appropriate to use to address the research problem or question of interest. For each description of a research question below, select the one corresponding statistical analysis technique most appropriate for addressing that research question. Question 7 Subquestions 7.a 0 point(s) The polling organization surveys 1000 people in a large community to assess if the percentage of people in the community living in a mobile home is more than 10%. Simple linear regression One-sample t-test for a population mean Paired t-test for a population mean difference Two-sample t-test for the comparison of two population means One-sample z-test for a population proportion Two-sample z-test for the comparison of two population proportions ANOVA for comparing many population means Chi-squared test of goodness of fit Chi-squared test of independence Chi-squared test of homogeneity 7.b 1 point(s) A polling organization surveys 1000 people in a large community to assess if the average number of hours that people watch television is more than 5 hours a day. Simple linear regression One-sample t-test for a population mean 8/11 4/17/2016 Paired t-test for a population mean difference Two-sample t-test for the comparison of two population means One-sample Z-test for a population proportion Two-sample Z-test for the comparison of two population proportions ANOVA for comparing many population means Chi-squared test of goodness of fit Chi-squared test of independence Chi-squared test of homogeneity 7.c 2 point(s) The polling organization surveys 1200 adults, records their age (in years) and how many hours they typically spend watching television per day, to assess if there is a significant relationship between age and hours of daily television viewing. Simple linear regression One-sample t-test for a population mean Paired t-test for a population mean difference Two-sample t-test for the comparison of two population means One-sample Z-test for a population proportion Two-sample Z-test for the comparison of two population proportions ANOVA for comparing many population means Chi-squared test of goodness of fit Chi-squared test of independence Chi-squared test of homogeneity 7.d 2 point(s) 9/11 4/17/2016 The polling organization polls people on a regular basis to monitor their changing confidence in the economy. The organization creates a numerical index (from 0 to 100) of confidence in the economy from answers to a questionnaire. Based on a random sample of people who were polled both in 2011 and again in 2012, the organization will assess if confidence in the economy changed from 2011 to 2012, on average. Simple linear regression One-sample t-test for a population mean Paired t-test for a population mean difference Two-sample t-test for the comparison of two population means One-sample Z-test for a population proportion Two-sample Z-test for the comparison of two population proportions ANOVA for comparing many population means Chi-squared test of goodness of fit Chi-squared test of independence Chi-squared test of homogeneity 7.e 0 point(s) The polling organization conducts a survey of adults between the ages of 30 and 50 years old to assess if there is an association between marital status (married, divorced, never-married) and smoking status (smoker, nonsmoker). Simple linear regression One-sample t-test for a population mean Paired t-test for a population mean difference Two-sample t-test for the comparison of two population means One-sample Z-test for a population proportion Two-sample Z-test for the comparison of two population proportions ANOVA for comparing many population means 10/11 4/17/2016 Chi-squared test of goodness of fit Chi-squared test of independence Chi-squared test of homogeneity Edit Assignment (/#!/students/56db9e5dac2a100b00bd213d/do) 57142d318bea840b00fac568 11/11