Stat 200 Final Exam Review Problems (1) (1)

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Stat 200 Name:____________________________________ Final Review Exam Directions: Do the following problems. Show all work. Round answers to 3-decimal places as appropriate, 1. The following data were obtained from a sample of construction companies who are all building 10- story structures. The survey asked how many full-time workers are employed on the building project. 152 163 142 110 198 125 173 212 200 165 158 Historically, 10-story structures are built on a budget which has a forecasted average employment of 175 full-time workers. At the α = .10 significance level, is there evidence that the mean number of full-time employees has changed. Include a p-value.

2. A new method of storing snap peas is believed to retain more ascorbic acid than an old method. In an experiment, snap peas were harvested under uniform conditions and frozen in 77 equal-size packages. Thirty five of these packages were randomly selected and stored according to the new method and the other thirty two packages were stored by the old method. Subsequently, ascorbic acid determinations were made, and the following summary statistics were calculated. New method Old method Mean 449 440 St. dev. 19 45 Sample size 35 42 Do these data substantiate the claim that more ascorbic acid is retained under the new method of storing? Test at  =.05. Provide a P-value. 3. Find the 95% Confidence interval for the data in problem #2.

4. The following summary statistics are recorded for independent random samples from two populations. Sample 1 Sample 2 n 1 = 19 n 2 = 16 ¯ x 1 = 16.01 ¯ x 2 = 17.59 1 2.34 s  2 2.37 s  Assuming normal populations, test if the population mean for the second population exceeds that of the first population. Use α = .01 . Provide a p-value.

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5. Find the 99% confidence interval for μ 1 − μ 2 where: Sample 1 Sample 2 n 1 = 19 n 2 = 16 ¯ x 1 = 16.01 ¯ x 2 = 17.59 1 2.34 s  2 2.37 s 

6. A study is to be made of the relative effectiveness of two kinds of cough medicines in increasing sleep. Six people with colds are given medicine A the first night and medicine B the second night. Their hours of sleep each night are recorded. Subject 1 2 3 4 5 6 Medicine A 4.8 4.1 5.8 2.9 5.3 8.4 Medicine B 3.9 4.2 5.0 4.2 5.4 8.0 Test whether there is a significance difference in the amount of sleep when switching from medicine A to medicine B using α = .05 . Provide a p-value. 7. Find the 98% confidence interval for the data in problem #6.

8. Government officials near a nuclear power plant have been working on an emergency preparedness program. In 2014, a random sample of 405 community residents was obtained and 275 said they were confident they would be notified quickly of a radioactive incident. In 2015, after the program started, a random sample of 388 community residents was obtained, and 310 felt they were confident they would be notified quickly of a radioactive incident. Test at the 10% significance level whether there is evidence that the true proportion of residents who were confident they would be notified quickly of a radioactive incident in 2015 is greater than in 2014. Provide a p-value. 9. Find the 72% Confidence interval for the data in problem #8.

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10. A survey of 600 households found that the family room was the primary television location in 415 homes. Test whether the true population proportion of households having the family room as the primary television location is actually less than .75 at the α = .05 significance level. 11. Find the 83% Confidence interval for the data in problem #10.

12. A company sells a strong commercial floor cleaner and claims that the flashpoint (the lowest temperature at which the vapor of a combustible liquid can be ignited in air) is 200ºF. A random sample of cleaner was obtained and the flashpoint of each was measured. For a sample of size 50 the sample mean was 198.2ºF and the sample standard deviation was 10ºF. At the α = .01 significance level, is there sufficient evidence to support the companies claim? Provide a p-value.

13. (For final review only, you do not need to do this problem on the Minitab project.) Mount McKinley in Alaska is one of the world’s most dangerous mountain peaks for climbers. On average, it takes 408 hours to traverse the 20,320 foot peak, with standard deviation 96 hours. a. Suppose 38 climbers are selected at random. Find the probability that sample mean time to climb this mountain is greater than 430 hours. b. For this group of climbers, find the value of c such that the probability the sample mean time is less than c is 0.05. (i.e. – find the 5 th percentile for traverse times.) c. If one climber is selected at random, find the probability that the mean time to climb the peak is between 305 and 495 hours.

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14. An instructor at Arizona State University asked a random sample of eight students to record their study times in a elementary statistics course. She then made a table for total hours studied over 2 weeks and test scores at the end of the 2 weeks. Here are the data: Study time 10 15 12 20 8 16 14 22 Test Scores 92 75 86 76 92 80 84 81 Fill in the appropriate blanks. Show all work below. a. Which variable is the explanatory variable?___________________________ b. Which variable is the response variable?______________________________ c. Assuming linearity, compute the correlation coefficient for these data_______________. d. Compute the least squares regression equation for the data________________________. e. Estimate the predicted test score for a student who studies 12 hours_________________.

15. A large organization is being investigated to determine if its recruitment is sex-biased. Tables 1 and 2, respectively, show the classification of applicants for sales and for secretarial positions according to gender and result of interview. Table 3 is an aggregation of the corresponding entries of Table 1 and Table 2. a. Calculate the χ 2 statistic for testing independence for each of the data sets given in Tables 1 and 2. Test the null hypothesis for independence for each using α = .01 b. Calculate the χ 2 statistic and test the null hypothesis for independence using the data in Table 3. c. Discuss why there is a difference in the results when the data is aggregated. Table 1 Sales Positions Offered Denied Total Male 25 50 75 Female 75 150 225 Total 100 200 300 Table 2 Secretarial Positions Offered Denied Total Male 150 50 200 Female 75 25 100 Total 225 75 300 Table 3 Secretarial and Sales Positions Offered Denied Total Male 175 100 275 Female 150 175 325 Total 325 275 600

For final review - BONUS. 17. Complete the following ANOVA table: Find F .05 from the table provided________________________ Conclusion (circle one): Reject H 0 Do not reject H 0 Source Sum of Squares Df Mean Squares F Treatment Error _______ 423.8 4 __ __________ __________ ______ Total 4719.4 14

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