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Dylan believes that male students in Math 171 are shorter than 6 feet (72 inches), on average. He selects a random sample of 40 of these students and measures their heights. He will use a one-sample -test to test analyze these data. Verify that the conditions on the sample are met to use this test.  

Below you are given the histograms of the test scores for three professors – Professor A, Professor B and Professor C – who teach large sections of statistics classes. Note that the histograms are drawn using the same scales for the horizontal and vertical axes. Please answer the following questions. a.  Which professor had the largest mean (largest average) test score for their students?  [largestmean] b.  What was the value of the largest mean, approximately?  [valuemean] c.  Which Professor had the most variation (largest standard deviation) in their test scores for their students? [mostvar] d.  Which Professor had the highest percent of students who earned a test score of 50 or lower?  [highpercent]    

Below is a boxplot of student exam scores a recent O.W.L. exam at Hogwarts for Professor Snape’s and Professor Sprout’s students.  Please answer the following questions. The middle 50% of Professor Sprout’s students’ scores were between (give answers as whole numbers)  [lower] and [upper].  

Below is a histogram of light bulb lifetimes from a simple random sample of 30 light bulbs. Note that the vertical axis is given in count (i.e., number of bulbs). Assume that no data point fell exactly on a class (i.e., bin) boundary. Please answer the following questions: a.  Which is the best descriptor of the “shape” of the distribution of light bulb lifetimes?  [shape] b.  The mean is [pickone] than the median.   c.  What percent of the light bulbs in the sample lasted less than 1100 hours? [percent]   d.  Which of the following classes contains the median light bulb lifetime?  [median]

Identify which hypothesis test is appropriate for each of the following scenarios. A local driver training school claims that at least 75% of its pupils pass the driving test on their first attempt. A sample of 60 students from the school are selected, and their performances on the driving test are noted. We wish to determine if the claim of the school is true. [prop] The daily wages in a particular industry are normally distributed with a mean of $13.20 and a standard deviation of $2.50. A company in this industry employs 40 workers and pays a daily wage, on average, of $12.20. We wish to determine if this company can be accused of paying inferior wages. [z] Suppose that the national average price for used cars is $10,192.  A manager of a local car dealership reviewed a random sample of 25 recent used car sales at the dealership and found the mean was $9750 and the standard deviation was $1400. We wish to determine if the price of used cars at the dealership differs from the national mean. [t] Starting salaries are determined for 40 female and 40 male electrical engineers. We wish to determine if male electrical engineers tend to have higher starting salaries than their female counterparts. [two]

Below is a boxplot of student exam scores a recent O.W.L. exam at Hogwarts for Professor Snape’s and Professor Sprout’s students. Use it to answer the following questions. a.  Which professor’s students had the smaller exam average (mean) score?  [mean] b.  Which professor’s students had more variation (i.e. a larger standard deviation) in their exam scores? [variation]

A farmer wished to determine which of two stimulants, A or B, is more effective in increasing the number of eggs laid by her chickens. She decided to test the hypotheses: 

Sugar consumption is a hot topic when it comes to good nutrition. Twelve-ounce cans of soft drinks often have 10 teaspoons of sugar in them. A random sample of 75 college students were asked how many cans of soft drinks they typically consume on a given day. That number was multiplied by 10 to give a daily amount of sugar (in teaspoons) consumed from soft drinks. The following statistics were calculated.

After once again losing a football game to the college’s arch rival, the alumni association conducted a survey to see if alumni were in favor of firing the coach.  A simple random sample of 200 alumni from the population of all living alumni were surveyed, and 105 of the alumni in the sample were in favor of firing the coach. Please answer the following questions. Be sure to show all calculator input for any partial credit. a.  Find a 90% confidence interval for the true proportion of living alumni who are in favor of firing the coach (please show all calculator input).  (2 points) b.  Verify you meet the conditions to use the interval you found in part (a).  (3 points) c.  Based on the confidence interval found in part (a), can the alumni association claim that the majority of alumni are in favor of firing the coach? Why or why not?  (3 points)

QUESTION 4 FOUR OPERATIONS Teneo’s students and teachers, on 23 April 2021,  celebrated World Book Day.  Solve the following  problems about World Book Day.