A scale measuring person's confidence in the media was administered to a sample of respondents. Is there a statistically significant difference between Democrats and Republicans in terms of their confidence in media? Higher scores on the scale indicate greater confidence. Use the five step model and write a sentence or two interpreting your results. Democrats X1 Republicans = 8.5 X2 s1 = 1.5 N1 = 36 = 7.8 s2 = 1.1 N2 = 35 Is there a statistically significant difference between males and females in terms of newspaper readership? The proportion of each sex that says they read a newspaper daily is reported below. Results are from a nationally representative sample. Use the five step model and write a sentence or two interpreting your results. Males Females Ps1 = 0.56 N1 = 786 Ps2 = 0.59 N2 = 965 Part 2. (2 POINTS). Ashville City Maintenance Chief wants to cut back on the costs of maintaining the city automobile fleet. Knowing that the city cars are kept for only year, he feels that the city's periodic maintenance schedule may cost more than it is worth. He randomly selects a sample of 300 cars. Among those 300 cars, 75 cars receive no maintenance unless they break down. The rest of the cars are maintained using the usual schedule. At the end of the year he finds the results pertaining to average costs per vehicle in these two groups (shown below). What can you tell the Ashville City Maintenance Chief about this experiment: is the difference across groups statistically significant at 95% confidence level? Use the five step model to answer this question. Write a sentence or two (using words, not just numbers!) summarizing your results for a wider audience. Variable \"Costs per Vehicle\": No Maintenance = $625 Maintained Cars = $575 S1 = 150 N1 = 75 S2 = 200 N2 = 225 X1 X2 SAMPLE ANSWERS 1 Part 2. Two sample hypothesis test Step 1. Making Assumptions 1. Samples 1 and 2 are random and independent. 2. Our variable is interval ratio (Score) 3. The sampling Z distribution is normal (our sample is large enough (N>120 for both samples together)) Step 2. Stating the Hypotheses Research Hypothesis: There is a difference between football and basketball players in the population. Null Hypothesis: There is no difference between football and basketball players in the population. Any difference observed between samples occurred by pure chance. Step 3. Drawing the Sampling Distribution and establishing a critical region. Zobtained=1.7 2 Step 4. Computing the test statistic Basketball X1 Football = 460 X2 s1 = 92 N1 = 102 = 442 s2 = 57 N2 = 117 X X s1 2 s 22 N 1 1 N 2 1 X X (92) 2 (57) 2 102 1 117 1 X X 8464 3249 101 116 X X 83.80 28.01 X X 111.81 X X 10.57 Z(obtained) ( X 1 X 2 ) (460 442) 18 1.70 X X 10.57 10.57 Step 5. Placing Z obtained on the distribution and stating the conclusion. Conclusion: Z obtained is not in the critical region (it is not higher than the Z critical). We fail to reject the null hypothesis with 95% confidence. It appears that there is no difference between football and basketball players in the population. Part 3. Two sample hypothesis test Step 1. Making Assumptions 1. Samples 1 and 2 are random and independent. 2. Our variable is a long ordinal scale (rating) 3. The sampling Z distribution is normal (our sample is large enough (N>120 for both samples together)) Step 2. Stating the Hypotheses Research Hypothesis: There is a difference between AA and Reg employees in terms of efficiency. Null Hypothesis: There is no difference between AA and Reg employees in terms of efficiency. Step 3. Drawing the Sampling Distribution and establishing a critical region. 3 -0.83 Step 4. Computing the test statistic Sigma = 2 2 S1 S2 8.41 4 + = + = 0.13=.36 N 11 N 21 96 99 Z(obtained) = 15.215.5 =0.83 0.36 Step 5. Placing Z obtained on the distribution and stating the conclusion. Conclusion: Z obtained is not in the critical region. We fail to reject the null hypothesis with 95% confidence. It appears that there is no difference between AA and Reg employees in terms of efficiency. Part 4. Two sample one tailed test Step 1. Making Assumptions 4 1. Samples 1 and 2 are random and independent. 2. Our variable is nominal (test of proportion) 3. The sampling Z distribution is normal (our sample is large enough (N>120 for both samples together)) Step 2. Stating the Hypotheses Research Hypothesis: The program resulted in a significantly lower divorce rate. Null Hypothesis: There is no difference in divorce rates across programs. Step 3. Drawing the Sampling Distribution and establishing a critical region. -0.76 -1.65 Conducting a one tailed test, with a negative tail (lower divorce rate). Step 4. Computing the test statistic Special Ps1 = .53 N1 = 78 Pu Regular Ps2 = .59 N2 = 82 N 1 Ps1 N 2 Ps 2 (78)(.53) (82)(.59) 41.34 48.38 0.56 N1 N 2 78 82 160 5 p p Pu (1 Pu ) Z (obtained) = N1 N 2 78 82 160 (.56)(.44) .2464 (.4964)(.1582) .079 N 1N 2 (78)(82) (6396) ( Ps1 Ps 2) .53 .59 .06 0.76 pp .079 .079 Step 5. Placing Z obtained on the distribution and stating the conclusion. Conclusion: Z obtained is not in the critical region. We fail to reject the null hypothesis with 95% confidence. It appears that there is no difference between the experimental and traditional programs in terms of divorce rates. 6