Statistics

8-14 :- In a 2012 survey, Gallup asked a sample of U.S. adults if they would prefer to have a job outside the home, or if they would prefer to stay home to care for the family and home. Partial results for the individuals who expressed a preference, broken down by gender, are displayed in the two-way table. Job Outside of the Home Stay at Home Total Male 391 ??? 504 Female 254 219 473 Total 645 332 977 8- Find the number of males who would prefer to stay at home. Ans: 504-391=113 or 332-219=113 9- What proportion of respondents would prefer a job outside of the home? Round your answer to two decimal places. Ans: 0.66 10- Compute the difference in the proportion of men who would prefer a job outside of the home and the proportion of females who would prefer a job outside of the home. Use two decimal places in your answer. 11- Use Statekey to calculate a 90% bootstrap percentile confidence interval for the difference in the proportion of men who would prefer a job outside of the home and the proportion of women who would prefer a job outside of the home. 12- Calculate a 90 % confidence interval for the difference in the proportion of men who would prefer a job outside of the home and proportion of women who would prefer a job outside of the home using the standard error (formula from ch 6). Show your work. How does it compare to your previous answer? 13- Are you justified in using the interval calculated in the previous problem? Explain briefly. 14- If you wanted to test to test the null hypothesis of no difference between men and women and you generated a randomization distribution to do that, where would that randomization distribution be centered? 15-19:- One of the symptoms of the flu is an elevated pulse rate. Pulse rates (in beats per minute) for n = 23 patients with the flu are provided. Sample size 23 Mean 89.348 Standard Deviation 7.854 Minimum 75 Q1 83.500 Median 90.000 Q3 93.000 Maximum 110 15- If you sketched a boxplot of the pulse rates, would there be any outliers? Explain briefly. Ans: Answers for IQR could vary slightly, depending on method/software used. Regardless, 110 should be the only outlier. Using Q1 and Q3 found in R: Use the 1.5IQR rule to detect outliers. IQR = 93 - 83.50 = 9.5 1.5IQR = 14.25 An observation is an outlier if it is smaller than 83.5 - 14.25 = 69.25 bpm or larger than 93 + 14.25 = 107.25 bpm. There is only one outlier, 110 bpm. 16- Find the z-score of someone with the flu who has a pulse rate of 78. 17- Interpret the z-score in the previous problem. 18- Give an interval that is likely to contain about 95% of the pulse rate. 19- Assuming this is a random sample of patients with the flu, find a 99% confidence interval for the mean pulse rate of all patients with the flue. 28-40:- The textbook dataset restaurant tips contains information of the tipping patterns of patrons of the First Crush bistro in north New York. The data from 157 bills include the amount of the bill, size of the tip, percentage tip, number of customers in the group, whether a credit card was used, day of the week, and a coded identity of the server. The data come from three different servers, coded as A, B, and C. The number of bill for each server is shown in the table. We would like to know if the servers serve equal numbers of customers. Server A B C Number of Bill 60 65 32 28- What are the null and alternative hypothesis? 29- If the null hypothesis is true, how many bill would we expect for each server? 30- Calculate the contribution to the chi-square statistic for server A. 31- What are the appropriate degrees of freedom for the chi-square distribution? 32- Use Statkey to calculate the chi-square statistic and p-value of the test. 33- At the 5 % significance level, what is your conclusion? 34- Is it appropriate to use chi-square distribution for these data? Explain briefly. We also have information on whether the bill was paid with cash or credit card, shown in the table below. We would like to know if there is an association between who the server is and whether the bill is paid with cash or credit card. What is the appropriate test to answer this question? Server A B C Total Cash 39 50 17 106 Credit Card 21 15 15 51 Total 60 65 32 157 35- What is the null hypothesis? 36- If the null hypothesis is true, how many bill server B would we expect to paid by cash? 37- What is the contribution to the chi-square statistics for the bills paid by cash to server B? 38- What are the appropriate degrees of freedom for the test? 39- Use statkey to calculate the test statistic and p-value of the test. 40- At the 5% significance level, what is your conclusion?