Tran is in charge of the school's Awards Dinner. She set up the multi-purpose room with a stage in front and round tables for parents, students, and family members to sit around for dinner. Below is the floor plan that she drew for the event Stage Question 9: The afternoon of the event, 214 people registered for the Awards Dinner. How many total tables will Tran need to set up? Explain how you found your answer
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Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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- 6. A research center claims that at least 30% of adults in a certain country think that their taxes will be audited. In a random sample of 1200 adults in that country in a recent year, 26% say they are concerned that their taxes will be audited. At α=0.10, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below. Question content area bottom Part 1 (a) Identify the claim and state H0 and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. enter your response here % of adults in the country think that their taxes will be audited. B. The percentage of adults in the country who think that their taxes will be audited is not enter your response here %. C. At least 30 30% of adults in the country think that their taxes will be audited. Your answer is correct. D. Less than…A pharmaceutical company claims that its new drug reduces systolic blood pressure. The systolic blood pressure (in millimeters of mercury) for nine patients before taking the new drug and 2 hours after taking the drug are shown in the table below. Is there enough evidence to support the company's claim? Let d=(blood pressure before taking new drug)−(blood pressure after taking new drug)d=(blood pressure before taking new drug)−(blood pressure after taking new drug). Use a significance level of α=0.1 for the test. Assume that the systolic blood pressure levels are normally distributed for the population of patients both before and after taking the new drug. Patient 1 2 3 4 5 6 7 8 9 Blood pressure (before) 185 160 187 192 204 203 203 196 203 Blood pressure (after) 166 151 170 186 181 194 179 175 181 Step 1 of 5: State the null and alternative hypotheses for the test. Step 2 of 5: Find the value of the standard deviation of the paired differences. Round your answer to one…A pharmaceutical company claims that its new drug reduces systolic blood pressure. The systolic blood pressure (in millimeters of mercury) for nine patients before taking the new drug and 22 hours after taking the drug are shown in the table below. Is there enough evidence to support the company's claim? Let d=(blood pressure before taking new drug)−(blood pressure after taking new drug)d=(blood pressure before taking new drug)−(blood pressure after taking new drug). Use a significance level of α=0.01α=0.01 for the test. Assume that the systolic blood pressure levels are normally distributed for the population of patients both before and after taking the new drug. Patient 1 2 3 4 5 6 7 8 9 Blood pressure (before) 198198 200200 159159 202202 185185 150150 148148 149149 175175 Blood pressure (after) 191191 174174 151151 178178 159159 140140 140140 141141 161161
- A pharmaceutical company claims that its new drug reduces systolic blood pressure. The systolic blood pressure (in millimeters of mercury) for nine patients before taking the new drug and 22 hours after taking the drug are shown in the table below. Is there enough evidence to support the company's claim? Let d=(blood pressure before taking new drug)−(blood pressure after taking new drug)d=(blood pressure before taking new drug)−(blood pressure after taking new drug). Use a significance level of α=0.05α=0.05 for the test. Assume that the systolic blood pressure levels are normally distributed for the population of patients both before and after taking the new drug. Patient 1 2 3 4 5 6 7 8 9 Blood pressure (before) 156156 155155 167167 176176 191191 160160 159159 197197 181181 Blood pressure (after) 146146 144144 154154 161161 165165 146146 148148 171171 155155 Copy Data Step 1 of 5 : State the null and alternative hypotheses for the test.A pharmaceutical company claims that its new drug reduces systolic blood pressure. The systolic blood pressure (in millimeters of mercury) for nine patients before taking the new drug and 22 hours after taking the drug are shown in the table below. Is there enough evidence to support the company's claim? Let d=(blood pressure before taking new drug)−(blood pressure after taking new drug)d=(blood pressure before taking new drug)−(blood pressure after taking new drug). Use a significance level of α=0.05α=0.05 for the test. Assume that the systolic blood pressure levels are normally distributed for the population of patients both before and after taking the new drug. Patient 1 2 3 4 5 6 7 8 9 Blood pressure (before) 156156 155155 167167 176176 191191 160160 159159 197197 181181 Blood pressure (after) 146146 144144 154154 161161 165165 146146 148148 171171 155155 Copy Data Step 2 of 5 : Find the value of the standard deviation of the paired differences. Round your answer to one…A research company has designed three different systems to clean up oil spillages. The following table contains the results, measured by how much surface area (in square meters) is cleared in 1 hour. The data were found by testing each method in several trials. Is there any significant difference in the testing of effectiveness of the three systems? Use the 0.05 level of significance. System A System B System C 293 295 304 298 291 290 301 302 299 294 287 295 297 300 - 293 - -
- a) write down the formula of the test statistic and find its value. b) Determine the rejection region and make a decision. c) Make a conclusion in the context of the problem.A small college has been accused of gender bias in its admissions to graduate programs.a. Out of 500 men who applied, 255 were accepted. Out of 700 women whoapplied, 240 were accepted. Find the acceptance rate for each gender. Does thissuggest bias?b. The college then looked at each of the two departments with graduate programsand found the data below. Compute the acceptance rate within each departmentby gender. Does this suggest bias? c. Looking at our results from Parts A and b, what can you conclude? Is theregender bias in this college’s admissions? If so, in which direction?A recent poll found that 664 out of 1026 randomly selected people in a particular country felt that colleges and universities with big sports programs placed too much emphasis on athletics over academics. Assuming the conditions for the CLT are met, use the accompanying Minitab output to complete parts a and b below. N Event Sample p 95% CI for p 1026 664 0.647173 (0.617934, 0.676413) Question content area bottom b. Suppose a sports blogger wrote an article claiming that a majority of adults from this country believe that colleges and universities with big sports programs place too much emphasis on athletics over academics. Does this confidence interval support the blogger's claim? Explain your reasoning. A. No, it is not a plausible claim because the confidence interval contains 50%. B. No, it is not a plausible claim because the confidence interval does not contain only values above 50%. C. Yes, it is a…
- Makers of generic drugs are required to show that their generic drugs do not differ significantly from the “reference” or brand name drugs that they imitate. One aspect in which the generic drugs might differ is their extent of absorption in the blood. Twelve subjects were available for the study. Six were randomly selected to receive the generic drug first and then, after a washout period, receive the “reference” drug. The remaining six received the “reference” drug first, followed by the generic drug after the washout period. Suppose the actual p-value for a two-sided test is 0.140. On the basis of this p-value, what should you conclude at α = 0.05? Group of answer choices The mean difference between the absorption rate of the reference drug and the absorption rate of the generic drug is equal to zero There is insufficient evidence to conclude that the mean difference between the absorption rate of the reference drug and the absorption rate of the generic drug is not equal to…Dr. V. noticed that the more frequently a student is late or absent from class the worse he or she performs on the final exam. He decided to investigate. Dr. V. collected a random sample of 22 students. This sample includes the number of times a student is absent and their grades on the final exam. The data can be found in the Excel file Assignment10_R1.xlsx on the Exercise1_Excel_Built-in f. worksheet. Do not use any software that I did not assign. Using Excel, conduct a NHST to determine whether there is a correlation in the population. Use a 0.05 significance level. Use the Excel file Assignment10_R1.xlsx, Exercise1_Correlation NHST worksheet) Write the Null & Alternate Hypotheses (Follow the examples shown in Clear-Sighted Statistics. Use the appropriate Greek letters and mathematical symbols). H0: H1: Write the Decision Rule using the Critical Value(s), not p-values. Calculate the value of the test statistic and the p-value.Dr. V. noticed that the more frequently a student is late or absent from class the worse he or she performs on the final exam. He decided to investigate. Dr. V. collected a random sample of 22 students. This sample includes the number of times a student is absent and their grades on the final exam. The data can be found in the Excel file Assignment10_R1.xlsx on the Exercise1_Excel_Built-in f. worksheet. Do not use any software that I did not assign. Using Excel, conduct a NHST to determine whether there is a correlation in the population. Use a 0.05 significance level. Use the Excel file Assignment10_R1.xlsx, Exercise1_Correlation NHST worksheet) Test Set-Up: What type of Null Hypothesis Test should you use? It this a left-tailed, two-tailed, or right-tailed test. Significance Level: Use a 5% significance level. What is/are the Critical Value(s)? Write the Null & Alternate Hypotheses (Follow the examples shown in Clear-Sighted Statistics. Use the appropriate…