# MA 3110 MA3110 Final Exam Answers (ITT TECH University)

MA3110 Final exam (ITT TECH)

1. On average, a doctor will treat between 0 and 5 patients a day. The random variable x represents the number of patients treated on a given day.

This probability distribution results in a mean score of approximately 2.57. How do you interpret the mean?

2. The Director of the Medical Board is interested in determining if it is “unusually low” for a doctor to treat one patient each day. The Director determines that the probability of a doctor treating 1 patient or fewer patients is 0.12. Based on the rules of using probabilities to determine when results are unusual, what should the director conclude?

3. Considering a standard normal distribution, find the area under the standard normal curve between z = -1.5 and z = 2.25

4. A car manufacturer is interested in determining the average braking distance for select tires under wintery conditions. He selects a random sample of select tires and assumes that the average braking distances are normally distributed. Which of the following would allow the manufacturer to reject the normality assumption?

5. Twenty randomly selected students took the statistics midterm exam. The results from the midterm show that we have a sample mean of 75 and a margin of error of 4.28. Construct the confidence interval for the mean score of all students.

6. A 95% confidence interval for the population proportion of adults that use a cell phone versus a land-line phone for their primary means of communications is 73.2% < p < 82.4%. Which answer choice best interprets the results of this confidence interval?

7. The P-value for a hypothesis test is P = 0.0325. What is your decision if your significance level is a= 0.05.

8. A restaurant owner wants to determine if there is enough evidence that the proportion of wait times to be seated in a restaurant is higher for group A than group B. If the samples that were obtained for each group are randomly selected and independent of one another, which test should the restaurant owner use to test the difference in wait times for group A and group B?

9. The table below shows a one-way analysis of variance with sample data that consists of measuring 5^{th} grade math scores from 12 randomly selected pages in 3 different textbooks.

10. Using the results from the ANOVA table above, what is the null hypothesis and what is the final conclusion?

11. A teacher wants to test whether the hours that a student spends studying online (independent variable) is correlated with the students test scores (dependent variable). To determine if the variables were correlated with the students test scores, the instructor calculated the correlation coefficient, r, of -0.831. What conclusion can the instructor make about the correlation of these two variables?

12. A study was done to determine whether shoe size and height correlated. It was found that there is a significant correlation between the two variables. Given that the equation of the regression line is ŷ = 1.87 + 51.36, where x = shoe size and ŷ = height in inches, what height would you predict for someone with a shoe size of 10?

13. A study shows that the number of crimes committed in a randomly selected city is uniformly distributed. The researcher randomly selected a city and randomly selected 2000 crimes from a recent year and conducted a goodness of fit test. The null hypothesis is the researcher’s claim that the distribution of the number of crimes is uniform. At a = 0.10, the test produced a X^{2} (chi squared) critical value of 17.275, a rejection region X^{2} > 17.275 and X^{2} test statistic of 10.32. What can you conclude from this goodness of fit test?

14. Below is a contingency table that contains the frequencies of 125 randomly selected criminal cases. The row variable identifies the conclusion of the trial (conclusion or no conviction) and the column variable identifies the plea (guilty or not guilty). Based on the table below, determine the percentage of criminal cases that ended in convictions and the plea was guilty.