Statistics Case Study-1 Age Weeks Employed 55 2130 1823 1152 3641 1925 1242 745 2525 640 2125 1325 1159 3449 2733 1835 20 a. Age Weeks Employed Mean 37. 75 Mean 18. 6875 Standard Error 2.

974195 Standard Error 2. 188452 Median 37. 5 Median 18. 5 Mode 25 Mode 21 Standard Deviation 11. 89678 Standard Deviation 8.

753809 Sample Variance 141. 5333 Sample Variance 76. 62917 Kurtosis -1. 17143 Kurtosis -0.

21626 Skewness 0. 337402 Skewness 0. 522601 Range 36 Range 30 Minimum 23 Minimum 6 Maximum 59 Maximum 36 Sum 604 Sum 299 Count 16 Count 16 Confidence Level (99. 0%) 8. 764138 Confidence Level (99. 0%) 6.

44877 b. 99% confidence interval estimate for mean age of newly hired employees; 37. 75! V 8. 76 = 28.

99 to 37. 75 + 8. 76 = 46. 51 c.

Hypothesis: Decision Rule: Reject Ho if t > t-critical Do not reject Ho if t < t-critical t-critical = t 0. 01, 15 = 2. 6020. 771 < 2. 602 Therefore, at a 99% Confidence Level the Null Hypothesis can not be rejected and we can not state that Riverside! |s mean duration of employment weeks is any greater than the mean duration of employment weeks within the rest of California. d.

Is there a relationship between the age of a newly employed individual and the number of weeks of employment? By using a scatter plot and plotting the number of weeks employed in respect to the ages of the workers, you can see that the points are distributed along a straight line. The number of weeks employed increase positively as the age of the worker increases. Therefore it is safe to say that there is a positive correlation between the ages of newly employed workers and the number of weeks they are employed. Textbook Exercise 7. 6, The Trash Bag Case Text Problem 7. 6: n = 40 mean = 50.

575 std dev. = 1. 6438 a. 95% = 0. 509408783 m = 50. 06559122 m = 51.

08440878 99% = 0. 669478969 m = 49. 90552103 m = 51. 24447897 b. Yes, we can be 95% confident that the trash bags are at least 50 pounds in strength because the lower confidence level is slightly more than 50 at 50. 06 pounds.

c. No, we can not be 99% confident that the trash bags are at least 50 pounds in strength because the lower confidence level is slightly less than 40 at 49. 9 pounds. d.

Even though I can not say for sure with 99% confidence that the trash bags have a 50 pound strength, the lower confidence level is very close at 49. 9 pounds. Since no other trash bag on the market has a breaking strength of 50 pounds, I think that I can say in good confidence that this bag is the strongest bag on the market. Textbook Problem 8.

76: a. , do not reject, the manufacturer! |s claim is true, reject the null, the manufacturer! |s claim is false. Sample size is > 30 so therefore we can use z-statistics. (316/400! V 0. 95) /[0. 95 (1-0.

95) /400]1/2 = -14. 683 So, if given a significant level (f~N), if z-stat < -Zf~N, then reject null hypothesis and accept alternative hypothesis. a -Zf~N Action on null hypothesis 0. 10 -1. 282 Reject 0. 05 -1.

645 Reject 0. 01 -2. 326 Reject 0. 001 -3. 090 Reject From the above information it can be concluded that the manufacturer! |s claim is false. c.

Not really because the manufacturer claims that their television sets last at least 5 years without needing repairs but the sample collected was from consumers that owned their sets for 5 years and not beyond. In order for the results of the survey to have practical importance we would need to sample consumers that have owned their sets for 5 or more years. Palmer vs. Woods: Woods, 1999 Palmer, 1960 mean = 69.

56 mean = 69. 95 N = 84 N = 112 std dev. = 2. 5 std dev. = 2.

5.