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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 0.18 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

A study was conducted and it found that the mean annual salary for all California residents was $63,783 and the true standard deviation for all California residents was $7,240. Suppose you were to randomly sample 50 California residents. Use this information to answer the following question.  What is the probability that the average salary for the 50 individuals in your sample would be at least $61,000? Make sure to type in your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was 0.54321 then you would type in 0.543.

Suppose a local pizzeria delivers pizzas every day of the week and their delivery times are normally distributed with a mean of 30 minutes with a standard deviation of 4 minutes. Determine the interval that contains the middle 80% of delivery times. Explain how you arrived at your answer.   Hint: Try sketching the normal distribution defined above and using percentiles, and shade the desired region Make sure to type your interval in an interval format with your bounds rounded to 2 decimal places. For example, if you thought the lower bound was 50.123 and the upper bound was 60.123 then you would type (50.12, 60.12) as your interval. 

How do we determine which measure of center is most appropriate for a given data set? Be as  specific as possible. 

A study was conducted and it found that the mean annual salary for all California residents was $63,783 and the true standard deviation for all California residents was $7,240. Suppose you were to randomly sample 50 California residents. Use this information to answer the following question.  What is the probability that the average salary for the 50 individuals in your sample would be at least $67,200? Make sure to type in your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was 0.54321 then you would type in 0.543.

A survey was taken of students enrolled in STEM classes at Taft College. One of the questions asked which city the students live in, and one of the other questions asked about their major. The results are shown below. Use them to answer the probability question that follows.  Probability Table Bakersfield Taft Shafter Other Math 3 5 2 4 Chemistry 9 4 1 5 Biology 4 13 8 6 Engineering  14 15 2 1 Physics 3 1 0 2   What is the probability that a randomly selected student from this survey is a biology major?    Make sure to type in your answer as a decimal rounded to 3 decimal places. For example, if you thought the answer was 0.12345 then you would type in 0.123. 

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 between 115 and 130?   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 where the heights of students in middle schools from around the county  were collected and analyzed. The data was normally distributed and they found that the mean height of those middle school students was 1.512 meters with a standard deviation of 0.07 meters.  Calculate the corresponding z-score for a student whose height was 1.6 meters tall.    Make sure to round your final answer to 3 decimal places. For example, if you thought the answer was 1.462178 then you would type in 1.462.

State all of the assumptions that are required for carrying out an ANOVA test as well as how you would check those assumptions. Be as specific as possible. 

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 28 students in his class and their final letter grades are shown below.  Distribution Table of Letter Grades Letter Grade Count/Frequency A 6 B Left Blank on Purpose C 11 D 4 F 1 Total 28 What percentage (relative frequency) of students received a B? Give your answer as a percentage rounded to 2 decimal places (i.e. If the answer is 17.43%, simply type in 17.43)