Mathematics > QUESTIONS & ANSWERS > Sophia stats milestone 5 MATHS questions with answers 2020/22 (All)

Sophia stats milestone 5 MATHS questions with answers 2020/22

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Select the 95% confidence interval for Mrs. Pellegrin's set of data. 9.4 to 10.52 9.53 to 10.39 9.34 to 10.44 9.48 to 10.44 RATIONALE In order to get the 95% CI , we first need to find the criti... cal t-score. Using a t-table, we need to find (n-1) degrees of freedom, or (5-1) = 4 df and the corresponding CI Using the 95% CI in the bottom row and 4 df on the far left column, we get a t-critical score of 2.776. We also need to calculate the mean: So we use the formula to find the confidence interval: The lower bound is: 9.96 -0.56 = 9.40 The upper bound is: 9.96+0.56 = 10.52 CONCEPT Confidence Intervals Using the T-Distribution 2 A school is gathering some data on its sports teams because it was believed that the distribution of boys and girls were evenly distributed across all the sports. This table lists the number of boys and girls participating in each sport. Boys Girls Tennis 18 30 Soccer 42 15 Swimming 12 18 Select the observed and expected frequencies for the boys participating in soccer. Observed: 42 Expected: 24 Observed: 42 Expected: 22.5 Observed: 57 Expected: 22.5 Observed: 57 Expected: 24 RATIONALE If we simply go to the chart then we can directly see the observed frequency for boys participating in soccer is 42. To find the expected frequency, we need to find the number of occurrences if the null hypothesis is true, which in this case, was that the three options are equally likely, or if the three options were all evenly distributed. First, add up all the options in the boys column: If each of these three options were evenly distributed among the 72 boys, we would need to divide the total evenly between the three options: This means we would expect 24 boys to choose tennis, 24 boys to choose soccer, and 24 boys to choose swimming. CONCEPT Chi-Square Statistic 3 What value of z* should be used to construct a 98% confidence interval of a population mean? Answer choices are rounded to the thousandths place. 1.175 2.055 1.645 2.325 RATIONALE Using the z-chart to construct a 98% CI, this means that there is 1% for each tail. The lower tail would be at 0.06 and the upper tail would be at (1 - 0.01) or 0.99. The closest to 0.94 on the z-table is between 0.9901 and 0.9898. 0.9898 corresponds with a z-score of 2.32. 0.9901 corresponds with a z-score of 2.33. Taking the average of these two scores, we get a z-score of 2.325. CONCEPT Confidence Intervals 4 A table represents the number of students who passed or failed an aptitude test at two different campuses. East Campus West Campus Passed 39 45 Failed 61 55 In order to determine if there is a significant difference between campuses and pass rate, the chi-square test for association and independence should be performed. What is the expected frequency of East Campus and passed? 48.3 students 50.5 students 42 students 39 students [Show More]

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