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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?

A local community college was interested in gauging how interested their students were in building a parking garage on campus. However, they knew that a large number of their students primarily took online courses, so they wanted to ensure that they compared the responses between students taking in-person classes and online classes. They decided to randomly survey 180 students taking in-person classes and 220 students taking online classes. They asked them whether or not they were interested in a parking garage being built on campus. Out of 180 students taking in-person classes, 108 of them stated they were interested. Out of the 220 students taking online classes, 117 mentioned they were interested.  Use this information to carry out the appropriate hypothesis test at the

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 21 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 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 26 students in his class and their final letter grades are shown below.  Distribution Table of Letter Grades Letter Grade Count/Frequency A 4 B 8 C Left Blank on Purpose D 3 F 1 Total 26 What percentage (relative frequency) of students received a C? Give your answer as a percentage rounded to 2 decimal places (i.e. If the answer is 17.43%, simply type in 17.43)

A study was conducted at a local community college was conducted to determine whether or not students were in favor of having a 1-week break in the fall semester over the Thanksgiving break. In order to accommodate the week long break, the fall semester would have to start 1 week earlier in the summer, and so the decision makers at the college wanted student’s opinions to see if they were in favor of the change. Out of the 110 students that were included in the survey, 63 stated that they were in favor of the week long break in the fall while 47 students were against that change.  Construct and interpret a 94% confidence interval for the true proportion of students at the school that are in favor of the change.   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 3 decimal places [i.e. (12.345, 45.678)] Make sure to include an interpretation in context of the given problem