vas conducted to investigate a relationship at injuries are independent of helmet color. Color of Helmet Yellow 27 White Red Blue 362 166 69 68 117 8 33
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- A case-control (or retrospective) study was conducted to investigate a relationship between the colors of helmets worn by motorcycle drivers and whether they are injured or killed in a crash. Results are given in the accompanying table. Using a 0.05 significance level, test the claim that injuries are independent of helmet color. Color of Helmet Black White Yellow Red Blue Controls (not injured) 479 346 32 164 88 Cases (injured or killed) 201 99 9 67 43A case-control (or retrospective) study was conducted to investigate a relationship between the colors of helmets worn by motorcycle drivers and whether they are injured or killed in a crash. Results are given in the accompanying table. Using a 0.05 significance level, test the claim that injuries are independent of helmet color. Black; White; Yellow; Red; Blue Controls (not injured) 500; 355; 32; 173; 79 Cases (injured or killed) 220; 115; 9; 71; 38Independent random samples of 32 people living on the west side of a city and 30 people living on the east side of a city were taken to determine if the income levels of west side residents are significantly different from the income levels of east side residents. Given the testing statistics below, determine if the data provides sufficient evidence to conclude that the income levels of west side residents are significantly different from the income levels of east side residents, at the 2% significance level. H0:μw=μeHa:μw≠μe t0=2.364 t0.01=±2.099 Select the correct answer below: No; the test statistic is not between the critical values. No; the test statistic is between the critical values. Yes; the test statistic is not between the critical values. Yes; the test statistic is between the critical values.
- Does It Pay to Plead Guilty? The accompanying table summarizes randomly selected sample data for San Francisco defendants in burglary cases (based on data from “Does It Pay to Plead Guilty? Differential Sentencing and the Functioning of the Criminal Courts,” by Brereton and Casper, Law and Society Review, Vol. 16, No. 1). All of the subjects had prior prison sentences. Use a 0.05 significance level to test the claim that the sentence (sent to prison or not sent to prison) is independent of the plea. If you were an attorney defending a guilty defendant, would these results suggest that you should encourage a guilty plea?A standardized math test was administered to two groups of 5th graders, one group sampled from classes whose teachers had followed the existing curriculum and one group sampled from classes whose teachers had followed a new curriculum, and the scores were compared using a t-test with the following results: t-test: Two-Sample Assuming Equal Variances Old Curriculum New Curriculum Mean 75.31914894 65.65957447 Variance 118.613321 801.1424607 Obervations 47 47 Hypothesized Mean Difference 0 df 92 t Stat 2.183587807 P(T<=t) one-tail 0.015768226 t Critical one-tail 1.661585397 P(T<=t) two-tail 0.031536452 t Critical two-tail…Independent random samples of 31 people living on the west side of a city and 25 people living on the east side of a city were taken to determine if the income levels of west side residents are greater than the income levels of east side residents. Given the testing statistics below, determine if the data provides sufficient evidence to conclude that the income levels of west side residents are greater than the income levels of east side residents, at the 2% significance level. H0:μw≤μeHa:μw>μe t0=0.511 t0.02=2.104 Select the correct answer below: Yes; the test statistic is greater than the critical value. No; the test statistic is greater than the critical value. No; the test statistic is less than the critical value. Yes; the test statistic is less than the critical value.
- A case control study was conducted to investigate a relationship between the colors of helmets worn by motorcycle drivers and whether they are injured or killed in a crash. Results are given in the accompanying table. Using a .01 significance level, test the claim that injuries are independent of helmet color. Blackhelmet white helmet Yellow helmet Red helmet Blue helmet Not injured 472 362 35 161 69 Injured 195 105 9 69 33The Youth Risk Behavior Survey (a study of public high school students) showed that 45 of 675 girls and 103 of 621 boys had been in a physical fight on school property one or more times during the past 12 months Using 5% significance, perform an appropriate test of hypothesis that the proportion of girlsinvolved in a physical fight on school property is less than the proportion of boys involved in a physical fight on school property.Step 1: H0: ________________ Ha: ____________________ Significance level α =0.05Step 2: Check necessary data conditions and compute an appropriate test statistic:Step 3: Compute corresponding p-valueA standardized math test was administered to two groups of 5th graders, one group sampled from classes whose teachers had followed the existing curriculum and one group sampled from classes whose teachers had followed a new curriculum, and the scores were compared using a t-test with the following results: Old Curriculum New Curriculum Mean 68.76595745 75.4893617 Variance 22.226642 33.8640148 Obervations 47 47 Hypothesized Mean Difference 0 df 88 t Stat -6.154501628 P(T<=t) 0.00 t Critical one-tail 1.662354029 P(T<=t) two-tail 0.00 t Critical two-tail 1.987289865 You decide to use the conventional p=.05 as your…
- A standardized math test was administered to two groups of 5th graders, one group sampled from classes whose teachers had followed the existing curriculum and one group sampled from classes whose teachers had followed a new curriculum, and the scores were compared using a t-test with the following results: Old Curriculum New Curriculum Mean 75.31914894 65.65957447 Variance 118.613321 801.1424607 Observations 47 47 Pooled Variance 459.8778908 Hypothesized Mean Difference 0 df 92 t Stat 2.1835887807 P(T<=)one tail 0.015768226 t Critical one-tail 1.661585397 P(T<=t) two-tail 0.031536452 t Critical two-tail 1.986086317 You decide to use the conventional p=.05 as your cutoff for statistical significance. What do you conclude from this analysis? a.…A standardized math test was administered to two groups of 5th graders, one group sampled from classes whose teachers had followed the existing curriculum and one group sampled from classes whose teachers had followed a new curriculum, and the scores were compared using a t-test with the following results: Old Curriculum New Curriculum Mean 65.06382979 66.5106383 Variance 822.4523589 127.5161887 Obervations 47 47 Hypothesized Mean Difference 0 df 60 t Stat -0.321814324 P(T<=t) 0.37 t Critical one-tail 1.670648865 P(T<=t) two-tail 0.75 t Critical two-tail 2.000297822 You decide to use the conventional p=.05 as your…Are low-fat diets or low-carb diets more effective for weight loss? This question was addressed in the article “Comparison of the Atkins, Zone, Ornish, and LEARN Diets for Change in Weight and Related Risk Factors Among Overweight Premenopausal Women: The A TO Z Weight Loss Study: A Randomized Trial” (C. Gardner, A. Kiazand, et al., Journal of the American Medical Association, 2007:969–977). A sample of 77 subjects went on a low-carbohydrate diet for six months. At the end of that time the sample mean weight loss was 4.7 kg with a sample standard deviation of 7.2 kg. A second sample of 79 subjects went on a low-fat diet. Their sample mean weight loss was 2.6 kg with a standard deviation of 5.9 kg. a) Can you conclude that the mean weight loss is greater for those on the low-carbohydrate diet? b) Can you conclude that the mean weight loss on the low-carbohydrate diet is more than 1 kg greater than that of the low-fat diet?
