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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 $1,430 and the sample standard deviation was $272. 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 professor at a local community college decided to try out a new lecture format for his statistics class, and he was curious how well students performed using this new format. So the professor decided to record every student’s final grade at the end of the semester to determine how effective this new lecture format was. There were 33 students in his class and their final letter grades are shown below.  Distribution Table of Letter Grades Letter Grade Count/Frequency A 6 B 9 C 11 D 4 F Left Blank on Purpose Total 33 What percentage (relative frequency) of students received an F? Give your answer as a percentage rounded to 2 decimal places (i.e. If the answer is 17.43%, simply type in 17.43)

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 98 6-10 43 11-15 24 16-20 12 21-25 6 26+ 3  

In 2018, a study was conducted that stated that the average commute time to work for Kern County residents was 22.6 minutes. Suppose you were hired to determine if the average commute time is different than it was in 2018. You randomly sample 87 individuals who commute to work from Kern county and you find that their average commute time was 23.7 minutes and you find the sample standard deviation of commute times for those 87 individuals was 3.6 minutes.  Carry out the appropriate hypothesis test at the

Consider a town where the average age of all individuals is 34.5 years old with a standard deviation of 12.2 years. Suppose you were to randomly select 50 individuals from this town as part of a study.  What is the probability that the average age of the 50 individuals in your study would be less than 38 years old or greater than 36 years old?

Dugan is taking Statistics and has just learned about confidence intervals. He makes the following statement: “If all other sample values are held constant, then increasing the confidence level from 90% to a higher percentage will always result in a wider confidence interval, regardless if you are dealing with means or proportions.” Do you agree/disagree with his statement? If you agree, then write a few sentences justifying why this statement is true. If you disagree, then provide a counterexample where this property doesn’t hold and specify which sample values you utilized. 

A recent study was conducted and it found that IQ’s are normally distributed with a mean of 100 and a standard deviation of 15. Use this information to find the following probability.  What is the probability that a randomly selected individual would have an IQ less than 97?   Make sure to write your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was 23.173% then you would type in 0.232.

A study was conducted that found 46.9% of all smartphone users in the US had an iPhone. Suppose you were to randomly sample 40 US smartphone users. What is the probability that at most 18 of them had an iPhone? Use a binomial distribution to answer this question. Make sure to round your answer to 2 decimal places; i.e. if your answer was 0.654321 then you would type 0.65

A recent study was conducted and it found that IQ’s are normally distributed with a mean of 100 and a standard deviation of 15. Use this information to find the following value below.  What IQ score would represent the 23rd percentile?   Make sure to write your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was 123.4567 then you would type in 123.457.

Suppose you construct a 90% confidence interval for the true population mean GPA of students at Taft College. If all of the sample values remained constant and you decreased the confidence level, what would happen to the width of your confidence interval?