Blog

Suppose you are interested in constructing a 95% confidence interval to determine the true proportion of residents in Kern County that are planning on voting for the republican candidate in the next presidential election. If you want to make sure that you are within 0.05 of the actual proportion, how many residents would you need to include in your sample? Reminder: It’s impossible to survey a fraction of a person

Suppose a study was conducted of community colleges in California to determine the average cost of tuition for in-state students. The study consisted of 45 community colleges from California. Based on the sample data, the average tuition was $1,410 and the sample standard deviation was $252. Use this information to construct and interpret a 92% confidence interval for the true average tuition of all California community colleges.    Make sure to address the following in your response: Check any and all relevant assumptions and state how you determined whether or not they were satisfied (Be as specific as possible) Make sure to type your confidence interval in an interval format with each bound rounded to the nearest whole number.  Make sure to include an interpretation in context of the given problem  

A study was carried out by a gaming company to try and determine the true proportion of teenagers that were interested in an upcoming video game they were releasing. The company decided to randomly survey 400 teenagers and they found that 162 of them were planning on purchasing the game when it comes out. Use this information to construct and interpret a 90% confidence interval for the true proportion of teenagers who plan to purchase the video game when it comes out. Make sure that you are addressing the following in your response.  Check any and all relevant assumptions and state specifically how they are/aren’t satisfied State the desired confidence interval (round any values in your interval to 2 decimal places, i.e. 54.321 would be rounded to 54.32) Interpret the interval in context of the scenario provided. 

A study was conducted on the fuel economy of vehicles in the U.S. The study found that cars that ran on gasoline averaged 24.2 MPG. Assume this data is normally distributed with a standard deviation of 3.7 MPG. Use this information to answer the following question.  What MPG would correspond to the 47th percentile of all cars in the US that run on gasoline? Make sure to round your answer to 2 decimal places; i.e. if your answer was 87.654321 then you would type in 87.65. 

A study was conducted on the fuel economy of vehicles in the U.S. The study found that cars that ran on gasoline averaged 24.2 MPG. Assume this data is normally distributed with a standard deviation of 3.7 MPG. Use this information to answer the following question.  What MPG would correspond to the 33rd percentile of all cars in the US that run on gasoline? Make sure to round your answer to 2 decimal places; i.e. if your answer was 87.654321 then you would type in 87.65. 

A study was conducted of college students that stated the true average number of units that a college student enrolls in each semester is 12.7 with a true standard deviation of 6.8. Suppose you randomly sampled 40 college students and recorded the number of units that each of them were enrolled in. Use this information to answer the following question.  What is the probability that the average number of units those students from your sample were enrolled in was less than 12.8.? Make sure to round your answer to 2 decimal places; i.e. if your answer was 0.54321 then you would type in 0.54. 

Isabella works for an insurance company and she is the director of the customer service department. One of her main goals is to reduce the wait times that customers experience when they call the department before they are connected to someone that can help them. She recorded all of the wait times that customers experienced in a given month and recorded it in the frequency distribution table below.  Suppose you were to construct a histogram based on this data (starting with the 0-5 minute group on the far left) identify what the overall shape of the data would look like.  Customer Wait Time Breakdown Minutes Spent Waiting Frequency 0 – 5 109 6-10 63 11-15 41 16-20 13 21-25 10 26+ 4  

The owner of a local restaurant was interested in figuring out the true proportion of their customers that eat at their restaurant on a monthly basis. They knew that they wanted to be accurate within 0.11 of the true actual proportion with 95% confidence. In order to meet these requirements, how large of a sample should they take? Make sure to round your answer properly since it is impossible to survey a fraction of an individual. 

A study was conducted in 2018 to look at average annual salaries for individuals who lived in Wisconsin. It found that on average individuals in Wisconsin earned $56,302 per year. Assume the true standard deviation for annual salary was $8,000. Suppose you took a random sample of 50 individuals from Wisconsin in 2018 and recorded their salaries. Use this information to answer the following question. What is the probability that the average salary for those 50 individuals in your sample would fall between $49,000 and $57,000 per year? Make sure to round your answer to 2 decimal places; i.e. if your answer was 0.54321 then you would type in 0.54. 

The CEO of a major tech company was interested in developing a new type of tablet. However, before she decided how much money she wanted to invest in research and development, she wanted to conduct a survey to determine the average amount of time a person spends on their tablet each day. She had her employees conduct a survey of 1000 randomly selected individuals who owned tablets. As part of the survey, they found that those 1000 individuals spent an average of 1.23 hours per day on their tablets. Assume the true standard deviation amount of time that someone spends on their tablet per day is 2.57 hours. Use this information to construct and interpret an 88% confidence interval for the true average amount of time a person spends on their tablet each day.  Make sure that you are addressing the following in your response.  Check any and all relevant assumptions and state specifically how they are/aren’t satisfied State the desired confidence interval (round any values in your interval to 2 decimal places, i.e. 54.321 would be rounded to 54.32) Interpret the interval in context of the scenario provided.