12. Suppose a researcher is using a two-way Chi-square test to evaluate the relationship between birth-order position and self-esteem. Each participant is classified as being 1* born, 2nd born, or 3rd born, and self- esteem is categorized as being low, medium, or high. In this study, the number of degree(s) of freedom (df) would be: A. 1 В. с. 3 2 D. 4
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- Do larger universities tend to have more property crime? University crime statistics are affected by a variety of factors. The surrounding community, accessibility given to outside visitors, and many other factors influence crime rate. Let x be a variable that represents student enrollment (in thousands) on a university campus, and let y be a variable that represents the number of burglaries in a year on the university campus. A random sample of n = 8 universities in California gave the following information about enrollments and annual burglary incidents.The owner of a chain of mini-markets has two stores, Store 1 and Store 2, in one city. She recently added a breakfast station in Store 1 and wants to determine if the mean daily sales of Store 1 is greater than the mean daily sales of Store 2. After choosing 12 days at random, she records the sales (in dollars) at Store 1 for these days. Then, she records the sales at Store 2 for these same days. The data and the differences (Store 1 minus Store 2) are shown in the table below. Day 1 2 3 4 5 6 7 8. 9. 10 11 12 Store 1 951 547 437 682 547 729 488 776 461 815 859 518 Store 2 989 599 500 680 451 528 452 741 446 758 960. 421 Difference (Store 1 − Store 2) −38 −52 63 2 96 201. 36 35 15 57 −101 97 Send data to calculator Send data to Excel (a)Are the two samples of daily sales amounts independent or paired…Consider a study that surveyed 50 people to rate how much they like their job. Ratings mean 1 for “hate my job”, 2 for “dislike my job”, 3 for “neutral”, 4 for “like my job” and 5 for “love my job”. This survey found that • 8 people hated their job• 14 people disliked their job • 15 people were neutral• 9 people liked their job, and • 4 people loved their job. (1) Write a description of the random variable describing this survey(2) Write a probability distribution describing the probability of the outcomes of this event. (3) What probability of people like their job?(4) Calculate the expected rating.
- 2. Metal Tags on Penguins and Survival. Data were collected over a 10-year timespan from a sample of 100 penguins that were randomly given either metal or electronic tags. One variable examined is the survival rate 10 years after tagging. The scientists observed that 10 of the 50 metal tagged penguins survived, compared to 18 of the 50 electronic tagged penguins. Test whether the survival rate is lower among metal- tagged penguins than among electronic-tagged penguins. Use subscripts E for Electronic and M for Metal. a. State hypotheses. b. Calculate the sample statistic PE - PM c. Use Normal distribution methods to calculate a z-test statistic, given SE = 0.0898. d. Find the p-value and draw a Normal curve with z-statistic and appropriate shaded region. Normal curve: p-value: e. State the conclusion of the test in context, using nontechnical language. f. Find a 90% confidence interval to three decimal places for this difference in proportions, given SE= 0.08836. Show your…Suppose that the average salary of health systems professionals is normally distributed with µ=KES 40,000 and σ = KES 10,000. What proportion of professionals will earn KES 24,800 or less? What proportion of professionals will earn KES 53,500 or more? What proportion of professionals will earn between KES 45,000 and KES 57,000? Calculate the 80th percentile. Calculate the 27th percentileThe impact of a low-calorie diet on laboratory mice's longevity is being investigated by a medical researcher. Twenty mice are split into two groups (E and F) by random. A typical diet is given to Group E, while Group F is given a diet that only contains 70% as many calories as Group E's diet. The length of life (in days) of each mouse over the 36-month trial is documented. Table 2 provides the data that was obtained. The symbol of double star (**) signifies that the mouse was still alive at the end of the investigation. (a) (b) (c) Table 2: The length of life (in days) of each mouse Group E 900 907 751 833 920 787 830 877 848 901 Group F 1037 905 1023 988 1078 1011 ** 1063 898 1033 State a suitable null and alternative hypotheses for the problem. At 5% significance level, test the hypotheses in part (a) by using an appropriate nonparametric test. Write your conclusion.
- Suppose you are conducting a paired t test to determine whether or not caffeine has an effect on heart rate. You have a sample of 60 participants and they ingest no caffeine each day for a week. At the end of the week, you measure their heart rates and find the mean. Then, the same 60 participants are given 500mg of caffeine every day for a week and again, at the end of the week you measure their heart rates and find the mean. What would the null hypothesis be for this test?Two popular brands of tires for tractor-trailers are the Puma and the Eternal. Salma is a buyer for a major shipping company and wants to determine if there is any difference between the two brands of tire in the mean distance (in thousands of km) driven on them before they need to be replaced. In the company's testing lab, Salma tests a random sample of 14 Puma tires and a random sample of 15 Eternal tires. (These samples are chosen independently.) For the Puma tires, the sample mean distance (in thousands of km) until they would need to be replaced is 54.71 with a sample variance of 5.95. For the Eternal tires, the sample mean distance (in km) until they would need to be replaced is 50.21 with a sample variance of 37.75. Assume that the two populations of distances driven are approximately normally distributed. Can Salma conclude, at the 0.05 level of significance, that there is a difference between the population mean of the distances (in thousands of km) driven on Puma tires before…What is Ha? (H0 is the mean VIQ scores for the younger, middle-aged, and older subjects are all not different from each other) (Note: 1= 5-25 Years, 2= 26-59 Years, 3= 60-92 Years) Multiple Choices: 1. H0 is not true 2. The mean VIQ scores for the younger, middle-aged, and older subjects 3. are all different 4. The mean VIQ scores for the younger, middle-aged, and older subjects are all different from each other 5. The mean VIQ scores for the younger, middle-aged, and older subjects are not equal to one another 6. The mean VIQ scores for the younger, middle-aged, and older subjects are not the same as each other
- The cumulative frequency below displays the amount of time (in minutes) taken to travel to work by employees at a shoe factory. 100 80 60- Cumulative frequency 40 20 10 30 40 Time (minutes) 20 50 60 70 80 90A researcher believes that there may be a negative association between the quantity of fertilizer used and the percentage of the population who live in rural areas in different countries. The data below shows the percentage of the population who live in rural areas and the fertilizer use measured in kg per hectare, for a random sample of 11 countries. 33%= 76kg, 6%=44kg, 58%= 6kg, 35%=68kg, 81%=3kg, 69%=10kg, 61%=7kg, 7%=176kg,74%=5kg, 71%=137kg, 17%=157kg Use the Spearman's rank order coefficient method to affirm or disagree with the researchers assumption.A student has completed 20 courses in the School of Arts and Sciences. Her grades in the 20 courses are shown below: A B A B C ссввв ВАВ Вв свсв А 1. Define a best variable name for the given data. (You must use the name in the Excel). 2. What is the type of variable?