These are all statistic questions. The questions are listed and all of them need to be answered. (please double check the answers so that they're correct. thank u)p.s I just want to know how much this would cost I might might just do it myself
1) label the Hypothesis Testing Model with the Critical values and Test Statistics 2) list any calculator function(s) you use with the appropriate values you used to answer the question. 3) round z scores & percentages to 2 decimal places and decimal probabilities to 4 decimal places. 1. A food manufacturer claims that their new low-fat oat bran muffin has a population mean fat content of 5 grams with a population standard deviation of 0.89 grams. A government food researcher believes the manufacturer's claim is too low and decides to test the manufacturer's claim. A random sample of 35 muffins yields a sample mean fat content of 5.3 grams. The food researcher decides to perform a hypothesis test at α = 5 % to determine if it is reasonable to reject the manufacturer’s claim. I. State the hypotheses (in words & symbols): H0:_______________________________________________________________ Ha:_______________________________________________________________ II. Determine the model to test H0 a) Can you use a normal distribution for the Sampling Distribution model to perform this test? Please explain. If not, then what distribution could you use? _________________________________________________________________ 2b) Using the appropriate notation, state the MEAN & STD ERROR of the sampling distribution: Mean:____________________________________________________________ STDError:__________________________________________________________ III. Determine the Decision Rule: State the decision rule: ____________________________________________________________ IV. Analyze the sample data: Using the appropriate notation, state the sample result of the test, p-value and the test statistic. sample result is:____________________________________________________ p-value is: ______________________________________________________ test statistic is: _____________________________________________________ V. State the Conclusion: ___________________________________________________ Answer Question: Do you believe that it is reasonable to agree with the researcher's claim at α = 5%? YOU MUST EXPLAIN YOUR ANSWER OTHERWISE: No credit will be given. _________________________________________________________________ 2. An FM rock station claims that 85% of all its listeners are college students. A statistician decides to test this claim against the suspicion that the percentage is too high. A random sample of 2000 listeners is selected from the population of all listeners and it is determined that 1655 are college students. Perform a hypothesis test to answer the question: Do the sample results support the statistician’s claim at α = 1 %? I. State the hypotheses (in words & symbols): H0:_______________________________________________________________ Ha:_______________________________________________________________ II. Determine the model to test H0 Can one use a normal distribution for the Sampling Distribution model to perform this test? Please explain. _________________________________________________________________ b) Using the appropriate notation, state the MEAN & STD ERROR of the sampling distribution: Mean:____________________________________________________________ STDError:__________________________________________________________ III. Determine the Decision Rule: State the decision rule: ________________________________________________________ IV. Analyze the sample data: Using the appropriate notation, state the sample result of the test, p-value and the test statistic. sample result is:____________________________________________________ p-value is: _________________________________________________________ test statistic is: _____________________________________________________ V. State the Conclusion: ___________________________________________________ Can the statistician reject the rock station's claim at α = 1%? YOU MUST EXPLAIN YOUR ANSWER OTHERWISE: No credit will be given. _________________________________________________________________ 3) A random sample of 900 M&Ms is selected from the population of plain M&Ms where the population proportion of red M&Ms is 35%. a) State the mean and standard error of the sampling distribution using the proper notation for the mean and standard error. _________________________________________________________________ b) Can the sampling distribution be approximated by a normal distribution? Show work to support your answer. _________________________________________________________________ c) Using the sampling distribution, calculate the probability that a sample of 900 M&Ms selected at random contains at least 37% red M&Ms. Draw graph and shade area representing the probability on the graph. Show work!! Show the calculator functions with input data that you used to solve this problem. 4) You are hired by a cell phone provider to determine the number of times per day their customers interact with their smartphone. You take a random sample of 25 customers and find the average number of interactions to be 75 times per day with a sample standard deviation of 5. 4 a. If you decide to construct a confidence interval for the population mean number of interactions, what distribution would you use and why? b. Construct a 99% confidence interval estimate for the population mean number of interactions. c. What is the margin of error for the confidence interval you found in part b? d. A representative for the cell phone provider told you they believe the mean number of interactions per day was 83. What would you say to the company representative? Explain. 5) A statistics student at a New York State community college, randomly samples 500 students who own cell phones to determine if they play games on their phones. 65% stated that they use their mobile phones to play games. Using this information, then: a) construct a 95% confidence interval (to 3 decimal places) for the population proportion, p, of NYS community college cell phone users who play games on their phones. b) construct a 99% confidence interval for the population proportion, p, of NYS community college cell phone users who play games on their phones. c) determine the margin of error for both the 99% and 95% confidence interval estimates. d) What did you notice about the relationship between the confidence interval width and the margin of error as the confidence interval increased from 95% to 99%? e) Would it be reasonable for someone to state that 75% of NYS community college cell phone users play games on their cell phones? YOU MUST EXPLAIN YOUR ANSWER OTHERWISE: No credit will be given. 6) The name of theorem that states: For any population, regardless of the shape of the population being randomly sampled, the sampling distribution of the mean can be reasonably approximated by a normal distribution whenever the sample size n is greater than 30. The theorem: 7) The Speedy Oil Change Company advertises that the average mean time it takes to change a customer's oil is 10 minutes. After receiving complaints from dissatisfied customers, the management at Speedy Oil Change headquarters hired a researcher to investigate the complaints to determine if the oil change took significantly longer than 10 minutes. The researcher randomly investigates 20 oil changing jobs and computes the sample mean time to change a customer’s oil is 11.3 minutes with a sample standard deviation of 3.3 minutes. Based on this sample result, the researcher decides to conduct a hypothesis test to determine if Speed Oil Change Company’s claim is statistically too low at α = 5 %? I. State the hypotheses (in words & symbols): H0:_______________________________________________________________ Ha:_______________________________________________________________ II. Determine the model to test H0 a) Can you use a normal distribution for the Sampling Distribution model to perform this test? Please explain. If not, then what distribution could you use? b) Using the appropriate notation, state the MEAN & STD ERROR of the sampling distribution: Mean:____________________________________________________________ STDError:__________________________________________________________ III. Determine the Decision Rule: State the decision rule: ____________________________________________________________ IV. Analyze the sample data: Using the appropriate notation, state the sample result of the test, p-value and the test statistic. sample result is:____________________________________________________ p-value is: ______________________________________________________ test statistic is: _____________________________________________________ V. State the Conclusion: ___________________________________________________ Answer Question: Based on this sample result, can the researcher conclude that Speed Oil Change Company’s claim is too low at α = 5 %? YOU MUST EXPLAIN YOUR ANSWER OTHERWISE: No credit will be given.