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MTH 231 Week 5 Final Exam Use this worksheet for your answers. Your score, based on the points shown for this exam in the rubric, will be corrected to the basis points shown for the final exam in the syllabus. Submit to the Assignments Section by 11:59 pm of the last day of class. Late work will not be accepted. 1. The following are the scores obtained by 30 students in epidemiology test: 83 67 94 77 55 82 79 72 88 65 81 63 92 61 85 71 79 70 89 52 66 63 75 84 99 81 73 79 68 77 a) Apply the Statdisk and look for the user-defined relative frequency histogram having a class width of 10 from 50. The labels must be “on�. Copy the histogram in this sheet. b) Look for the Normality Assessment using the Statdisk. Does it show the sample from the normal population? Are the results from the histogram and the test results the same with regard to normality? What did you apply for the alpha level of the test? 0 c) Refer to the Statdisk, get the descriptive statistics of the data below: Mean Median Standard Deviation Range
Midrange d) Sarah got 79 in her exam. The z-score is shown below: 0.2927 2. The die rolled once with the events as shown: A: Event F: Roll an even number B: Event J: Roll 1, 2, 3, or 4 a) Define the term mutually exclusive. There are two events which are independent and the existence of the first event has nothing to do with the existence of another. b) What set has mutually exclusive events? A, B, Both, or Neither? A 3. Every person at St. Goodenough Hospital is categorized as below average, average, or above average with regard to the understanding. They are also divided as fair, good, or excellent. The evaluation is shown below: ----Potential for Advancement---Prof. Knowledge Fair Good Excellent Below Average 16 12 22 Average 45 60 45 Above Average 93 72 135 a) Get the probability of the chosen employee at random having the excellent potential advancement. b) Get the probability of the person being selected at random who is having an average or above average professional knowledge, as well as excellent potential advancement. 4. Correctly, what is the Central Limit Theorem (CLT)? Explain in full detail why is it essential? 1) When the samples of size of at least 30 came from random population, then the sampling distribution have an estimated normal distribution; 2) If the population is distributed accordingly, then the sampling distribution have a normal distribution as well. 3) For any kind of sample size, the population is normally distributed. 4) This is beyond the result of CLT, than the accurate statement of it. The CLT is essential because it provides the sampling distribution of the sample means. 5. Indicate whether each statement is valid with a “Yes” or “No.” a. Under particular limitations, the binomial distribution can be estimate by the normal distribution allowing us to apply the normal distribution for computation with the binomial distribution.
b. As what has been stated in CLT, the sampling distribution of the sampling mean estimates the normal distribution in a manner that it may not enhance the size of the given samples. c. The CLT may not be used until the population probability distribution become identifiable. d. No proof was used in CLT. It still a hypothesis 6. The post anaesthesia care area (recovery room) at St. Luke’s Hospital in Pflugerville, Ontario, was broadened. The move will mean that the mean number of people per day can also be enlarged. A random sampling was conducted in order to determine the patients coming after the broadening. 25 27 25 26 25 28 28 27 24 26 25 29 25 27 24 a What is the null hypothesis? The mean number of patients per day arrived to be 25 or less. b What is the alternative hypothesis? The mean number of patients per day will be greater than 25 c What specific test will you use to test the hypotheses at ι = 0.05? t-test d What is the p-value for the test? p = 0.0087 e Interpret the meaning of this p-value. The probability of arriving with the test statistics is 2.6935 if the null hypothesis holds to be true. This is the value used in t-statistic excluding the null hypothesis. f What is the critical value for the test? (Assume ι = 0.05.) cv = 1.7613 g Interpret the meaning of this critical value. If we like to manipulate the type I error to become 0.05 or lesser, then the greatest value for the test should be1.7613. There must be more explanation here. h Is there sufficient statistical evidence at the 0.05 significance level to reject the null hypothesis? Yes, because the p-value is less than 0.05. i Is this a right-tail test, left-tail test, or two-tail test? Right-tail test 7 Choose one best answer among the given options. a) There are a lot of values b) A range of values is formulated from the given data in order to present the parameyers inside the range at a particular probability: a confidence interval (1) the population parameter (2) a point estimate (3) the mean of the population c) What affects the sample error aside from the standard deviation? a confidence interval (1) the population parameter (2) the point estimate
(3) the sample size d) For example, you have 100 sample population, for every sample you establish 95% confidence interval for the mean. WE are right to assume that 95% of the confidence interval is one of the following: (1) a sample mean (2) the population mean (3) a point estimate (4) the standard deviation of the population e) The t-distribution is applied if the population has one of the following aside from having a normal distribution: (1) the population standard deviation is unknown (2) the population standard deviation is known (3) the mean of the population is unknown (4) the point estimate is known 8 As part of the protocol, the Keystone Police selected 65 ambulances and inspect their tires. The sample mean for this was 32 32 lbs/sq. in. While the standard deviation was 2lbs/sq. in. Get the 98% confidence interval of said population. You may refer to Statdisk. a Confidence Interval: b Margin of Error: c With a larger sample size, would you expect the margin of error to increase or decrease? 9 Get the right and precise response for the following: a) Define correlation analysis b) In what manner that the dependent variable in correlation is being determined? What is the other term for it? c) In what manner that the dependent variable in correlation is being determined? What is the other term for it? Based on the study, the independent variable pertains to the value that can changed and controlled by the research. It is assumable variable in the research. d) Is there causality present on both variables? Explain The relationship of the two variables does not indicate any causality, it only suggests that there is a linear relationship existing in both variables, but does not show any kind of causality. 10 Look for the incorrect portion among the statements below about the coefficient of correlation a) It can cover from -1 to +1. b) The square is the coefficient of identification. c) It pertains to the rate of variation discussed.
d) It is a shows the relationship between two variables. 11 A research was formulated about the automobile speeds of a particular model and the outcome fuel consumption rank. Think that the data provided below was randomly gathered. Refer to the Statdisk in order to answer the statements below. a. Calculate the coefficient thru the Statdisk b. Explain the outcome of your computation Speed MPG 45 33 52 32 49 28 60 26 67 22 61 21 a What is the coefficient or correlation and interpret and define it as well r = -0.877 b What is the coefficient of determination and describe it as well. r2 = 0.769 c Identify the relationship of speed and mpg in layman’s term referring to the result of your computation. It suggests that there is a negative correlation exiting on speed and mpg d What statistic should we use in order to get the variance? 76.9% of can be explained by the regression model. 12 Immediately after the 9-11 incident, America Online conducted a survey about: the reestablishment of World Trade Center. The responses are the following: Yes - 768,731 No -286,756 Too soon to decide The respondents who participate is of large number, is it the representation of the entire US population? 13 What level of measurement should be used on the following: (nominal, ordinal, interval, ratio) a) The weight of the airplane passengers b) How the doctor describe the following: “abstains from alcohol, light drinker, moderate drinker, heavy drinker” ¬¬¬¬¬¬¬¬¬¬¬¬¬¬ c) The questions about the emotions of people during the day ranging from 1-10 scale d) The following colors: red, blue, white, tan, black, yellow