A fine dining restaurant claims that the group sizes of their customers follows the following distribution:2 реople3 реople4 people4+ people40%10%20%30%Gustavo, a waiter at the restaurant, would like to test this claim. He takes a sample of 96 customers and records the observed frequencies in the following table:2 реople3 реople4 people4+ people396.2724(a) In performing this statistical test, state the hypotheses.O Họ: the distribution of customers for each group is the same as the observed frequencies vs. HA: the distribution of customers for each group is not thesame as the observed frequenciesO Ho: the distribution of customers for each group is not the same as claimed by the restaurant vs. HA: the distribution of customers for each group is thesame as claimed by the restaurantO Ho: the proportions of customers for each group are all the same vs. HA: the proportions of customers for each group are not all the sameO Ho: the distribution of customers for each group is not the same as the observed frequencies vs. HẠ: the distribution of customers for each group is thesame as the observed frequenciesO Họ: the distribution of customers for each group is the same as claimed by the restaurant vs. HA: the distribution of customers for each group is not thesame as claimed by the restaurant(b) What is the expected frequencies of each group? Fill out the table. (Round your answers to 2 decimal places, if needed.)2 рeople3 people4 people4+ people(c) What is the test statistic value for this hypothesis test? (Round your answers to 2 decimal places, if needed.)TS = (d) The test statistic follows a chi-square distribution with df = 4(e) Using the statistical table, the p-value is 0.025 < p-value < 0.05 +(f) Based on the p-value, those conducting the test should fail to reject + the null hypothesis at the significance level of 0.05.(g) What is the appropriate conclusion?O There is sufficient evidence to conclude the distribution of customers for each group is the same as claimed by the restaurant.O There is insufficient evidence to conclude the proportions of customers for each group are not all the same.O There is sufficient evidence to conclude the proportions of customers for each group are not all the same.O There is sufficient evidence to conclude the distribution of customers for each group is not the same as claimed by the restaurant.O There is insufficient evidence to conclude the distribution of customers for each group is not the same as claimed by the restaurant.

a) The hypotheses are: H0: The distribution of customers for each group is the same as claimed by…

Answered: A fine dining restaurant claims that…

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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2. A study for adverse reactions assigned adults at random to one of two common pain relievers (ibuprofen and acetaminophen). It was found that out of 733 adults who were administered ibuprofen, 103 of them experienced an adverse reaction, and out of 732 adults who were administered acetaminophen, 85 of them experienced an adverse reaction. Let p1 denote the proportion of adults who experience an adverse reaction when taking ibuprofen and let p2 denote the proportion of adults who experience an adverse reaction when taking acetaminophen. Suppose we want to answer the following questions. i) Test, at the 3% level of significance, whether the proportion of adults who experience an adverse reaction when taking ibuprofen is greater than the proportion of adults who experience an adverse reaction when taking acetaminophen. ii) Calculate the 97% confidence interval for p1 - P2. The table below provides the information needed to perform the hypothesis test: Value x1 103.0000 85.0000 733.0000…
..... ..... ..... ..
A survey described the results of a poll of working adults in Canada. Each person in a random sample was classified according to gender and the number of vacation days he or she usually took each year. The resulting data are summarized in the given table. Days of Vacation Gender Male Female None 51 42 1-5 21 25 6-10 67 79 11-15 106 98 16-20 71 70 21-25 82 58 More than 25 118 79 (a) Is it reasonable to conclude that there is an association between gender and the number of vacation days taken?Test the appropriate hypotheses using a 0.05 significance level. Calculate the test statistic. (Round your answer to two decimal places.)?2 =
2. A study for adverse reactions assigned adults at random to one of two common pain relievers (ibuprofen and acetaminophen). It was found that out of 733 adults who were administered ibuprofen, 103 of them experienced an adverse reaction, and out of 732 adults who were administered acetaminophen, 85 of them experienced an adverse reaction. Let p1 denote the proportion of adults who experience an adverse reaction when taking ibuprofen and let p2 denote the proportion of adults who experience an adverse reaction when taking acetaminophen. Suppose we want to answer the following questions. i) Test, at the 3% level of significance, whether the proportion of adults who experience an adverse reaction when taking ibuprofen is greater than the proportion of adults who experience an adverse reaction when taking acetaminophen. ii) Calculate the 97% confidence interval for p1 - P2. The table below provides the information needed to perform the hypothesis test: Value x1 103.0000 85.0000 733.0000…
A governmental agency computed the proportion of violent crimes in the United States in a particular year falling into each of four categories. A simple random sample of 500 violent crimes committed in California during that year were categorized in the same way. The following table presents the results. Category U.S.Proportion CaliforniaFrequency Murder 0.018 4 Forcible Rape 0.07 35 Robbery 0.390 218 Aggravated Assault 0.522 243 Can you conclude that the proportions of crimes in the various categories in California differ from those in the United States as a whole? Use the 0.05 level of significance and the P-value method with the TI-84 Plus calculator. (b) Find the P-value. Round the answer to at least four decimal places.
2. A study for adverse reactions assigned adults at random to one of two common pain relievers (ibuprofen and acetaminophen). It was found that out of 733 adults who were administered ibuprofen, 103 of them experienced an adverse reaction, and out of 732 adults who were administered acetaminophen, 85 of them experienced an adverse reaction. Let p1 denote the proportion of adults who experience an adverse reaction when taking ibuprofen and let p2 denote the proportion of adults who experience an adverse reaction when taking acetaminophen. Suppose we want to answer the following questions. i) Test, at the 3% level of significance, whether the proportion of adults who experience an adverse reaction when taking ibuprofen is greater than the proportion of adults who experience an adverse reaction when taking acetaminophen. ii) Calculate the 97% confidence interval for p1 - P2. The table below provides the information needed to perform the hypothesis test: Value x1 103.0000 85.0000 733.0000…
A random survey of health issues, conducted by the Department of Public Health of the Commonwealth of Massachusetts, examined the results from the state's seven largest cities. These cities were selected on the basis of their diverse racial and ethnic populations. The percentage of adults with diabetes in each city in the survey is given in the following table. City Boston Worcester Springfield Lowell Fall River Lawrence NewBedford Adults withDiabetes (%) 4.2 5.2 9.1 5.7 8.1 7.9 6.3 Find the average percentage of adults with diabetes in these seven cities. (Round your answer to two decimal places.) %What is the standard deviation for these data? (Round your answer to two decimal places.) %
Use the following scenario to answer the next 6 questions: M&Ms are your favorite vending machine snack and you purchase them often. Lately, it seems like the bags have been having a disproportionate distribution of the colors. The company claims that 24% of the candies per bag should be blue. You decide to test this claim for yourself. You purchase a large bag and find that 38 of the 224 candies are blue. Before complaining to the company, you want to be fairly sure of your accusation, so you set a 1% significance level for your test. Do you have sufficient evidence that the color distribution is different than advertised? Based on the data, the value of the test statistic is:

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