Sophia Statistics Unit 5 Milestone Questions and Answers with Complete Solutions

phia :: Welcome https://www.sophia.org/spcc/introduction-to-statistics-2/milestone_take_feedbacks/4324532 1/22 UNIT 5 — MILESTONE 5 Score 19/24 You passed this Milestone 19 questions were answered correctly. 5 ques ...

phia :: Welcome https://www.sophia.org/spcc/introduction-to-statistics-2/milestone_take_feedbacks/4324532 1/22 UNIT 5 — MILESTONE 5 Score 19/24 You passed this Milestone 19 questions were answered correctly. 5 questions were answered incorrectly. 1 Joe is measuring the widths of doors he bought to install in an apartment complex. He measured 72 doors and found a mean width of 36.1 inches with a standard deviation of 0.3 inches. To test if the doors differ significantly from the standard industry width of 36 inches, he computes a z-statistic. What is the value of Joe's z-test statistic? 2.83 -1.81 -2.83 1.81 RATIONALE 6/29/2020 Sophia :: Welcome https://www.sophia.org/spcc/introduction-to-statistics-2/milestone_take_feedbacks/4324532 2/22 If we first note the denominator of Then, getting the z-score we can note it is This tells us that 36.1 is 2.83 standard deviations above the value of 36. Note that when you round some values you may get slightly different results, but the results should be relatively close to this final calculated value. CONCEPT Z-Test for Population Means 2 Emile has calculated a one-tailed z-statistic of -1.97 and wants to see if it is significant at the 5% significance level. What is the critical value for the 5% significance level? Answer choices are rounded to the hundredths place. -2.33 0 -1.04 -1.64 RATIONALE Recall that when a test statistic is smaller than in a left-tailed test we would reject Ho. The closest value to 5%, or 0.05, in the table would be between 0.0505 and 0.495. 0.0505 corresponds with a z-score of -1.64 0.0495 corresponds with a z-score of -1.65. We need to calculate the average of the two z-scores to get a z-score of -1.645. CONCEPT How to Find a Critical Z Value 3 6/29/2020 Sophia :: Welcome https://www.sophia.org/spcc/introduction-to-statistics-2/milestone_take_feedbacks/4324532 3/22 What do the symbols , , and represent? Variables of interest Defined variables Population parameters Sample statistics RATIONALE Recall that is the sample proportion, is the sample mean, and is the sample standard deviation. Since all of these come from samples they are statistics. CONCEPT Sample Statistics and Population Parameters 4 A coin is tossed 50 times, and the number of times heads comes up is counted. Which of the following statements about the distributions of counts and proportions is FALSE? The distribution of the count of getting heads can be approximated with a normal distribution. The distribution of the count of getting tails can be approximated with a normal distribution. The count of getting heads is a binomial distribution. The count of getting heads from a sample proportion of size 20 can be approximated with a normal distribution. RATIONALE 6/29/2020 Sophia :: Welcome https://www.sophia.org/spcc/introduction-to-statistics-2/milestone_take_feedbacks/4324532 4/22 If we look at the counts from a large population of success and failures (2 outcomes), this is called a binomial distribution, not a normal distribution. CONCEPT Distribution of Sample Proportions 5 Henri has calculated a z-test statistic of -2.73. What is the p-value of the test statistic? Answer choices are rounded to the thousandths place. 0.003 0.004 0.394 6/29/2020 Sophia :: Welcome https://www.sophia.org/spcc/introduction-to-statistics-2/milestone_take_feedbacks/4324532 5/22 0.006 RATIONALE If we go to the chart and the row for the z-column for -2.7 and then the column 0.03, this value corresponds to 0.0032 or 0.003. CONCEPT How to Find a P-Value from a Z-Test Statistic 6 Keith tabulated the values for the average speeds on each day of his road trip as 61.5, 62.2, 55.7, 50.6, 71.3, 70.8, and 66.8 mph. He wishes to construct a 90% confidence interval. What value of t* should Keith use to construct the confidence interval? Answer choices are rounded to the thousandths place. 1.895 6/29/2020 Sophia :: Welcome https://www.sophia.org/spcc/introduction-to-statistics-2/milestone_take_feedbacks/4324532 6/22 1.415 1.943 1.440 RATIONALE Recall that we have n = 7, so the df = n-1 = 6. So if we go to the row where df = 7 and then 0.05 for the tail probability, this gives us a value of 1.943. Recall that a 90% confidence interval would have 10% for the tails, so 5% for each tail. We can also use the last row and find the corresponding confidence level.