Blog

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.

Exam Question 10 Let  represent the Covid vaccination rate in Rancho Cucamonga. The null and alternative hypotheses are , . Given this information, write the claim being tested. Sandy tests the claim and finds the P-value to be 0.03. Write the conclusion in plain language if the level of significance is 1%.

Prof Rea’s Exam Question 4. Show as much work as possible and clearly show all four steps of a hypothesis test to earn credit: Last year, researchers determined that adults in the US spent an average of 152 minutes on social media per day. You wonder if the amount of time people have been spending on social media has increased since last year. You randomly survey 120 adults in the US and find that they spend an average of 145 minutes on social media per day. You compute the sample standard deviation to be 35 minutes. Test your claim using a 5% level of significance. Round all calculated values to three decimal places.

Exam Question 4 IQ is normally distributed with a mean of 110 points and a standard deviation of 13 points. Einstein’s IQ is 3.8 standard deviations above the mean. What is Einstein’s IQ? Is it unusual? Explain how and why or why not. Find the proportion of people with an IQ of at most 130. 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 60% of the population. His solution is below. Describe two errors he made and explain to him how to fix them.