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Exam Question 7 The following table shows the number of people who developed Covid-19 in a sample of 94 total participants who developed Covid-19. Participants are organized by their reported gender and whether they received a vaccine or placebo in the trial.  Vaccine Placebo Total Male 4 42 46 Female 3 36 39 Other 1 8 9 Total 8 86 94 What is the probability of someone with a vaccine developing Covid-19? To earn full credit, write your answer using probability notation, as a fraction and decimal rounded to three decimal places. What is the probability that someone who is male and vaccinated develops Covid-19? To earn full credit, write your answer using probability notation, as a fraction and decimal rounded to three decimal places. A student answers the following question incorrectly. Explain the mistake they made and answer the question correctly (use proper notation and justify your answer with a calculation).  Question: Is it more likely to meet a man with a placebo that developed Covid-19 or a woman with a placebo that develops Covid-19? Answer: Since there are more men who received the placebo than women, you are more likely to meet a man with a placebo that developed Covid-19. What is the probability that someone who is male or vaccinated develops Covid-19? To earn full credit, write your answer using probability notation, as a fraction and decimal rounded to three decimal places.

Exam Question 5 The two given distributions have the same mean. Without doing any calculations, identify which distribution has less variability. Explain why you think this.  a.   b.

You will now upload your Work and Answer Template here. Change your Work and Answer Template to ONE pdf file and send it to your computer. Click the RED “Start Assignment” button. Click the “Choose File” button and select your file. Click the RED “Submit Assignment” button again. Make sure your file was uploaded successfully (you may see confetti!). Click the button at the bottom of this question where it says “I have successfully uploaded my work and answer template pdf file and am ready to click “Submit Quiz” at the bottom of the page.” Click the “Submit Quiz” button at the bottom of the page to finish/submit this assessment DO NOT CLICK SUBMIT QUIZ UNTIL YOU HAVE SUBMITTED THE ASSIGNMENT AND SEE CONFETTI

Prof Rea’s Exam Q12 A roulette wheel has 18 red numbers, 18 black numbers, and 2 green numbers. So, the proportion of red numbers is 0.474, the proportion of black numbers is 0.474, and the proportion of green numbers is 0.052. The table below gives the frequencies with which the ball landed on each color in 200 trials. Do the results suggest that the wheel is out of balance? Perform a goodness of fit test using a 5% level of significance. Step 1: Form your hypotheses.  Step 2: Calculate the expected frequencies and verify that the criteria for the Chi-Square distribution is satisfied. Color Observed frequency Expected frequency red 84 black 106 green 10 Step 3: Calculate the test statistic. Round each term to four decimal places. Use the test statistic to find the P-value rounded to four decimal places. You may use this desmos graph to compute the P-value. Step 4: State the conclusion in the context of the problem.

1. This assessment is enabling you to demonstrate your understanding elementary statistics. Use techniques you have learned to solve all problems on the assessment. Points will be earned primarily through the process of solving. Therefore, you will show as much work as possible and will provide justification whenever necessary. Use models, tables, and/or write descriptively when providing explanations. Write your favorite topic from the class in the left-hand bottom corner of the first page. Write something down, even if you don’t know the final answer. The solutions you provide should be of your own original thought. No collaboration/discussion with anyone is permitted or use of any computer system or server, is allowed. Desmos is permitted on this assessment. Please write the desmos function used if you do. If I suspect any part of the work is not your own, you will earn a zero on the assessment and the activity will be reported to the college to be formally processed and permanently recorded. Sign your name on your work and answer template to acknowledge and agree to these terms. 

Prof Rea’s Exam Question 3. Show as much work as possible and clearly show all five steps of building a confidence interval to earn credit: You wonder how much time, on average, people are spending on social media. You randomly survey 150 adults in the US and find that they spend an average of 180 minutes on social media per day. You compute the sample standard deviation to be 40 minutes. Construct and interpret a 95% confidence interval for the mean time (in minutes) that adults in the US spend on social media. Round all calculated values to three decimal places.

Upon treatment with heat or chemicals, bacteria will _______________________.

Exam Question 4 IQ is normally distributed with a mean of 110 points and a standard deviation of 13 points. Kelso’s IQ is 2.1 standard deviations below the mean. What is Kelso’s IQ? Is it unusual? Explain how and why or why not. Find the proportion of people with an IQ of at least 120. Write probability notation in your answer and write the desmos function you used to do the calculation. Round Z-scores to two decimal places. Round your answer to three decimal places. Alfred wants to know the IQ’s of the people who encompass the middle 80% of the population. His solution is below. Describe two errors he made and explain to him how to fix them. Lower limit is and the upper limit is .  So 80% of all IQ’s are between 25.8 points and 194.2 points.

Prof Rea’s Exam Question 2. A restaurant is deciding which farm to order berries from for a seasonal dessert on their menu. The average cost for a pound of berries in California is $2.82 with a population standard deviation of $0.45. Assume that berry cost in California is normally distributed. Suppose that farms in California sell 10 different kinds of berries.  Explain why the sampling distribution of sample means is approximately normal.  Compute the mean,

Prof Rea’s Exam Question 6. A scientist takes a swab for a patient to determine if they are sick with Strep. The scientist’s null hypothesis is given as follows:  : The patient has no indication that there is any bacteria present in the culture and can therefore be deemed healthy. Describe the type II error that could occur in context.