Sophia Statistics Milestone 5,

Mrs. Pellegrin has weighed 5 packages of cheese and recorded the weights as 10.2 oz, 10.5 oz, 9.3 oz, 9.8 oz, and 10.0 oz. She calculated the standard deviation to be 0.45 oz. 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 critical 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.