Sophia Statistics Unit 5 Milestone.pdf

Which of the following is an example of a parameter? Half of the receipts at the coffee shop include web address for giving feedback. 9047 out of 531,310 citizens voted in the special election for city council. 3.5% of the restaurant goers are given a survey to fill out. All of the members of the community watch group gave their availability to volunteer over the summer. RATIONALE Recall a parameter comes from the entire set of interest, the population. Since they are looking at all members of a community here, their availability to volunteer would be an example of a parameter. CONCEPT Sample Statistics and Population Parameters I need help with this question 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: 22.5 Observed: 42 Expected: 24 Observed: 57 Expected: 24 Observed: 57 Expected: 22.5 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 I need help with this question 3 Sukie interviewed 125 employees at her company and discovered that 21 of them planned to take an extended vacation next year. What is the 95% confidence interval for this population proportion? Answer choices are rounded to the hundredths place. 0.11 to 0.21 0.10 to 0.23 0.16 to 0.17 0.11 to 0.16 RATIONALE In order to get the CI we want to use the following form. p with hat on top plus-or-minus z to the power of asterisk times square root of fraction numerator p with hat on top q with hat on top over denominator n end fraction end root First, we must determine the corresponding z*score for 95% Confidence Interval. Remember, this means that we have 5% for the tails, meaning 5%, or 0.025, for each tail. Using a z-table, we can find the upper z-score by finding (1 - 0.025) or 0.975 in the table. This corresponding z-score is at 1.96. We can know p with hat on top comma space q with hat on top comma space a n d space n. So putting it all together: The lower bound is: 0.168-0.065 =0.103 or 0.10 The upper bound is: 0.168+0.065 =0.233 or 0.23 CONCEPT Confidence Interval for Population Proportion I need help with this question 4 Select the statement that correctly describes a Type II error. A Type II error occurs when the null hypothesis is accepted when it is actually false. A Type II error occurs when the null hypothesis is rejected when it is actually true. A Type II error occurs when the null hypothesis is accepted when it is actually true. A Type II error occurs when the null hypothesis is rejected when it is actually false. RATIONALE Recall a Type II error is when we incorrectly accept a false null hypothesis. In this case, we want to reject and conclude there is evidence is correct. CONCEPT Type I/II Errors I need help with this question 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. 0.004 0.006 0.003 0.394 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 I need help with this question 6 One condition for performing a hypothesis test is that the observations are independent. Marta is going to take a sample from a population of 600 students. How many students will Marta have to sample without replacement to treat the observations as independent? 540 60 120 300 RATIONALE In general we want about 10% or less to still assume independence. So size = 0.1*N = 0.1(600) = 60 A sample of 60 or less would be sufficient. CONCEPT Sampling With or Without Replacement I need help with this question 7 Brad recorded the number of visitors at the local science museum during the week: Day Visitors Tuesday 18 Wednesday 24 Thursday 28 Friday 30 He expected to see 25 visitors each day. To answer whether the number of visitors follows a uniform distribution, a chi-square test for goodness of fit should be performed. (alpha = 0.10) What is the chi-squared test statistic? Answers are rounded to the nearest hundredth. 2.54 1.40 3.36 1.12 RATIONALE Using the chi-square formula we can note the test statistic is CONCEPT Chi-Square Test for Goodness-of-Fit I need help with this question 8 What value of z* should be used to construct a 97% confidence interval of a population mean? Answer choices are rounded to the thousandths place. 2.17 1.65 1.88 1.96 RATIONALE Using the z-chart to construct a 97% CI, this means that there is 1.5% for each tail. The lower tail would be at 0.015 and the upper tail would be at (1 - 0.015) or 0.985. The value of 0.9850 is actually on the z-table exactly. 0.9850 corresponds with a z-score of 2.17. CONCEPT Confidence Intervals I need help with this question 9 Mike tabulated the following values for heights in inches of seven of his friends: 65, 71, 74, 61, 66, 70, and 72. Mike wishes to construct a 95% confidence interval. What value of t* should Mike use to construct the confidence interval? Answer choices are rounded to the hundredths place. 1.94 2.37 4.58 2.45 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 0.025 for the tail probability, this gives us a value of 2.447 or 2.45. Recall that a 95% confidence interval would have 5% for the tails, so 2.5% for each tail. We can also use the last row and find the corresponding confidence level (see 95%). CONCEPT How to Find a Critical T Value I need help with this question 10 The data below shows the grams of fat in a series of popular snacks. Snack Grams of Fat Snack 1 9 Snack 2 13 Snack 3 21 Snack 4 30 Snack 5 31 Snack 6 31 Snack 7 34 Snack 8 25 Snack 9 28 Snack 10 20 If Morris wanted to construct a one-sample t-statistic, what would the value for the degrees of freedom be? 9 5 10 11 RATIONALE The degrees of freedom for a 1 sample t-test are df=n-1 where n is the sample size. In this case, n=10, then df = n- 1 = 10-1 = 9. CONCEPT T-Tests I need help with this question 11 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 -1.64 -1.04 0 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 I need help with this question