M8 Problem Set

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M8: Problem Set Due No due date Points 5 Questions 5 Time Limit None Attempt History Attempt Time Score LATEST Attempt 1 11,690 minutes 5outof 5 Score for this quiz: 5 out of 5 Submitted Sep 16 at 10:02pm This attempt took 11,690 minutes. Question 1 0/0 pts A company would like to determine if there is a difference in the number of days that employees are absent from the East Side Plant compared to the West Side Plant. So, the company takes a sample of 54 employees from the East Side Plant and finds that these people missed an average of 5.3 days last year with a standard deviation of 1.3 days. A sample of 41 employees from the West Side plant revealed that these people were absent an average of 6.8 days last year with a standard deviation of 1.8 days. a) Find the 96% confidence interval for estimating the difference in the population means (Jq - Y2). b) Can you be 96% confident that there is a difference in the means of the two populations? c) Interpret the results. Your Answer: A.
Iny =54,ny =41,8; = 1.3,8, = 1.8,71 = 5.3,72 = 6.8 _ 32 7 = ~ (B1 —Z2) 24/ —+ = <pp —p2 < (B1 —Z2) + 24/ + ni N2 |(5.3 6.8) 2.05\/ L& 4 L8 < 1 pp < (5.3 6.8) + 2.054 |—2.181 < p1 pg < —.8192 B. 96% confident that there is a difference in the mean of the two population. C. Due to the confidence interval being negatve, 96% confident that there is a difference in the mean of the two population. Therefore, people on the West Side will be missing more than people from the East Side Plant. 4 4
Solution. When we look back at table 6.1, we see that 96% confidence corresponds to z=2.05. If we say that the East Side Plant corresponds to population 1 and the West Side Plant corresponds to population 2, then: n4{=54, n,=41, s1=1.3, s,=1.8, x% = 5.3, Xxd = 6.8, a) We will use eqn. 8.1: L 51 8550 o s T x—x)—z’—+—+< —h <(X—%)+z | —+ (x; —x; n ", W —Hy < —X;) n n, 132 182 132 182 +— <y —p; <(53-68)+ 2.05 |— + O —08) 203 feep Sy et A -2181 < J; |, <—.8192 b) Notice that the entire 96% confidence interval is negative (it is never positive or zero). Therefore, we can say that we are 96% confident that there is a difference in the two population means. c) Since the entire confidence interval is negative, we can be 96% confident that (u1 - y2) is negative. This means that on average, people from the West Side Plant will be absent more days than people from the East Side Plant. Question 2 0/0pts Seven students take a speed reading course in order to improve their reading ability. The reading scores of the seven before and after taking the course are given below: Person 1 2 3 4 5 6 7 x Test Score (Before) 350 371 360 400 450 389 410 y Test Score (After) 370 366 365 413 440 420 419 Note that n = 7. We will define dq = x4 - y4. After doing the appropriate calculations, we find that .
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d =—9 s;,= 14.12. Find the 80 % confidence interval for mean of the differences, Jg. Your Answer: Sd Sd ‘d—t% < g <d+t% a 14.12 B 14.12 9 L441B <y < 9+1.44—fi‘ =9 7.69 < pg < —9+7.69) ‘—16.69 < pg < —1.31\ Solution. When we look at the student’s t chart for 80% confidence (the 80% Is found along the bottom row of the chart) and df=7-1=6 (the 6 is found in the leftmost column) we find that t=1.44. Then Sd vn = S4 = d—t—Sreiigad ¥ t Vn 14.12 14.12 —9- 144 —— < p, < -9+ 144 —— V7 V7 —9-7.69 < py <—9+ 7.69 —16.69 < py < —1.31 Question 3 0/0 pts A company wants to buy new accounting software for its employees. It must decide between software A and Software B. The company will decide between the two software packages based on how quickly its employees can learn how to use the software. So, seven employees are
chosen to test the software packages. The number of hours that it takes each employee to learn each software package is given by: Employee 1 2 3 4 5 6 7 x Hours to learn Software A 27 33 22 40 37 38 25 y Hours to learn Software B 30 36 25 4 37 35 23 Note that . We will define , d4 = x4 - y4. After doing the appropriate calculations, we find that. d=-1143 s;= 2.80. Find the 80 % confidence interval for mean of the differences, Mg. Your Answer: d—t=% d+t—=< \/fi<,uld< + 7 ~ ~ {44280 _ 2.80 1.143 14428 <y < 1.143+1.44fi‘ |—1.143 1.523 < pg < —1.143 + 1.523| ‘—2.67 < pg < .381 Solution. When we look at the student’s t chart for 80% confidence (the 80% is found along the bottom row of the chart) and df=7-1=6 (the 6 is found in the leftmost column) we find that t=1.44. Then Sd vn 3 Sa d—t—<|.ld<d+t Vn 2.80 2.80 —1. 43— 1A~ iy <1143 144 —— V7 V7 —1.143 - 1.523 < py; < —1.143 + 1.523 —2.67 < p, < .381
Question 4 0/0 pts Consider the following dependent random samples: Observations 1 2 3 4 5 6 7 8 9 10 x-values 153 160 163 168 171 158 157 166 170 155 y-values 158 162 165 163 17.7 161 163 17.0 173 152 a) Do hypothesis testing to see if ug < 0 at the a =.025. Your Answer: HO:Hd:OH1:Md<O t = d = —23 —1.99 Left tailed test, DOF=10-1=9, | g25 = 2.262
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Solution. Since we are testing whether or not ud < 0, then our null and alternate hypothesis will be set as follows: Ho: ug =0 Hi:pg <0 Note n=10. If we calculate d4 = x4 —V4, ..., d10 = X410 Y10- Then find the mean of the d’s, we get d* = -.23. The standard deviation, Syq = .3653. -l d t= = = (sa/yn) (3653 /,10) =159 This is a left-tailed test. So, for DOF=10-1=9 we have t.qo5 = 2.262. Since this is a left-tailed test, we will reject the null hypothesis if the test statistic t (-1.99) is less than negative Ta (-2.262). Since t;s not less than -t.go5, we do not reject the null hypothesis. Question 5 513 pts As a reminder, the questions in this review quiz are a requirement of the course and the best way to prepare for the module exam. Did you complete all questions in their entirety and show your work? Your Answer: Yes Quiz Score: 5 out of 5