Assessment – Hypothesis TestingDIRECTION: For each of the given problems, conduct a hypothesis test (assume that theunderlying population is normally distributed).1. ATMS must be stocked with enough cash to satisfy customers making withdrawals over an entireweekend. But if too much cash is unnecessarily kept in the ATMS, the bank is forgoing the opportunityof investing the money and earning interest. Suppose that at a particular branch, the population meanamount of money withdrawn from ATMS per customer transaction over the weekend is Php8,000, witha population standard deviation of Php1,500. a. Ifa random sample of 36 customer transactions indicatesthat the sample mean withdrawal amount is Php8,600, is there evidence to believe that the populationmean withdrawal amount is no longer Php8,000? (Use a 0.05 level of significance.)2. A research done by a graduating student reports that the average score of University students in statisticscourse is less than 80. To test this claim, a random sample of 10 students was taken and their scores inthe course are recorded as: 65, 70, 80, 85, 60, 90, 80, 75, 85, 90. At 0.05 level of significance, test thevalidity of this claim.3. A research study was conducted to compare two methods of teaching statistics in graduate school. Onemethod, called the traditional method, presented the course without the use of statistical software. Theother method, referred to as experimental method, taught the course and utilized statistical softwareextensively. The scores made on a common comprehensive final exam by the students in both classesare shown in the table below.86 7789 90 85Traditional8285 82738273797186909881Experimental 78 83 96 898368 8483768377At 5% significance level, determine whether there is a sufficient statistical evidence to indicate that theexperimental method is more effective than the traditional method.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Philosophical and health issues are prompting an increasing number of Taiwanese to switch to a vegetarian lifestyle. A study published in the Journal of Nutrition compared the daily intake of nutrients by vegetarians and omnivores living in Taiwan. Among the nutrients considered was protein. Too little protein stunts growth and interferes with all bodily functions; too much protein puts a strain on the kidneys, can cause diarrhea and dehydration, and can leach calcium from bones and teeth. Independent random samples of 51 female vegetarians and 53 female omnivores yielded the following summary statistics, in grams, on daily protein intake. Vegetarians: ?" = 39.04, ? = 18.82, ? = 51 Omnivores: ?" = 49.92, ? = 18.97, ? = 53 Do the data provide sufficient evidence to conclude that the mean daily protein intakes of female vegetarians and female omnivores differ? Perform the required hypothesis test at the 1% significance level. Assume equality of variances. Determine a 99%…
.A new, miracle diabetes drug that diminishes major symptoms of diabetes has been approved by the FDA. Health care professionals and researchers believe that the new drug will prolong lifespan of diabetes patients. If the population is in steady state and the incidence is constant, what will the effect of this new drug be on the prevalence of diabetes in the population? Explain.
1. ABC inc. stock is currently selling for $30, one year from today the stock price can either increase by 20% or decrease by 15%. The probability of an increase in the stock price is equal to 0.3. The one-year risk-free rate is 5% What is the value of a European put that expires in one year with an exercise price of $24. 2. Graphically, show the value and the profit and loss of the following butterfly position: Long in a call with an exercise price of $30, short in 2 calls with an exercise price of $45, and long in a call with an exercise price of 60. All calls are written on the same stock and have the same maturity. 3. "Early exercise of an American option on a stock that does not pay any dividend is not optimal regardless of whether the option is a Call or a Put". True, False, or Uncertain. Explain.
The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 9.7% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. Before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine. Assuming his suspicion that 9.7% of his customers buy a magazine is correct, what is the probability that exactly 6 out of the first 13 customers buy a magazine? 0.000305894 0.00100664 0.000699781 0.000778757 0.000204114 0.000326183
The medical community unanimously agrees on the health benefits of regular exercise, but are adults listening? During each of the past 15 years, a polling organization has surveyed americans about their exercise habits. In the most recent of these polls, slightly over half of all American adults reported that they exercise for 30 or more minutes at least three times per week. The following data show the percentages of adults who reported that they exercise for 30 or more minutes at least three times per week during each of the 15 years of this study. Year Percentage of Adults Who Exercise 30 or more minutes at least three times per week 1 41.1 2 45 3 47.2 4 45.6 5 46.5 6 44.4 7 47.7 8 49.9 9 48 10 49 11 50 12 52.2 13 50.7 14 54.5 15 52.3 use simple linear regression to find the parameters for the line that minimizes MSE for this time series. Do not round your interim computations and…
Consider the following data: Stock M N Average return 26% 16% Risk (Std. Dev.) 20% 10% If the return on stocks M and N are perfectly negatively correlated, what is the range of risk (std dev) associated with all possible portfolio combinations? A. Range of the risk: between 0= risk s10 % OB. Range of the risk: between 0 < risk 10% OC. Range of the risk: between 5% and 10%. OD. Range of the risk (std. dev): between 15% to 20% OE. None of the above
Borrowing money may be necessary for business expansion. However, too much borrowed money can also mean trouble. Are developing countries tending to borrow more? A random sample of 20 developing countries gave the following information regarding foreign debt per capita (in U.S. dollars, inflation adjusted). (Reference: Handbook of International Economic Statistics, U.S. Government Documents.) Country 1 2 3 4 5 6 7 8 9 10 Modern Debt per Capita 175 152 125 124 95 83 34 29 21 89 Historic Debt per Capita 147 134 86 113 58 62 33 36 49 72 Country 11 12 13 14 15 16 17 18 19 20 Modern Debt per Capita 23 28 18 29 197 189 144 124 102 71 Historic Debt per Capita 24 12 12 29 106 156 145 119 118 76 Does this information indicate that foreign debt per capita is increasing in developing countries? Use a 0.01 level of significance. (a) What is the level of significance? Compute the sample test statistic. Find the P-value of the sample test statistic.
(a)Consider a flight with a seating capacity of 160 seats. This flight is always full and there is a chance to be overbooked. The actual no-show rate (NSR) of the flight is 3.5% and the estimated NSR is 6.3%. If this flight is oversold according to the estimated NSR, what is the number of excess/extra passengers that will show up and there will be no seats for them on the day of departure? (b)Consider a flight with a seating capacity of 160 seats. This flight is always full and there is a chance to be overbooked. The actual no-show rate (NSR) of the flight is 3.5% and the estimated NSR is 6.3%. If the one-way fare of this flight is $300. If this flight is oversold according to the estimated NSR, what is the additional revenue that this flight will generate due to overbooking?
4. When the Titanic sank in 1912, there were over 1,300 passengers aboard. A random sample of 50 passengers that were aboard is taken. The amount they paid for the voyage and whether or not they survived is recorded. A model is fit to predict the probability they survived when the ship sank is obtained. Survived Logistic Fit of Survived By Fare 1.00 0.75 0.50- 0.25- 50 4 Parameter Estimates 100 Term Intercept -1.404254 0.4353289 Fare 0.01246686 0.0097945 For log odds of Yes/No Fare Estimate Std Error ChiSquare 10.41 1.62 150 200 Prob> ChiSq 0.0013 0.2031 No Yes a) Suppose someone paid a fare of 25 pounds. Predict the probability they survived. b) How much would someone pay to have at least a 65% chance of survival?
The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 8.7% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. Before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine. (b) Assuming his suspicion that 8.7% of his customers buy a magazine is correct, what is the probability that exactly 3 out of the first 14 customers buy a magazine? Give your answer as a decimal number rounded to two digits.
Recent revenue shortfalls in a southern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 20%20% tuition increase. It was determined that such a large increase was needed to simply compensate for lost support from the state. Random samples of 100 freshmen, 100 sophomores, 100 juniors, and 100 seniors from the university were asked whether they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university’s budget at current levels. The results are given in the table. Strongly opposed Freshman Sophomore Junior Senior Yes 78 72 58 36 No 22 28 42 64 What is the contribution to the chi‑square statistic from the cell of strongly opposed juniors? = 0.1551 =3 =9 =0.1475
3. Scenario It is believed that large doses of acetaminophen (the active ingredient in over the counter pain relievers like Tylenol) may cause damage to the liver in nearly half of those tested. A researcher wants to conduct a study to estimate if the proportion of acetaminophen users who have liver damage is the same as previously reported. For participating in this study, he will pay each subject $20 and provide a free medical consultation if the patient has liver damage. Part A If he wants to limit the margin of error of his 98% conﬁdence interval to 2%, what is the minimum number of subjects he needs? (answer should be in the form of x,xxx) the minimum amount of money he needs to set aside to pay his subjects? $ (answer should be in the form of $xx,xxx) Part B The amount you calculated in Part A is substantially over his budget so he decides to use fewer subjects. Will this change increase or decrease the width of his conﬁdence interval? Will this new confidence interval be…

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