It is claimed that an industrial safety program is effective in reducing the loss of working hours due to factory accidents. The following data are collected concerning the weekly loss of working hours due to accidents in six plants both before and after the safety program is instituted. Do the data substantiate the claim ?

person |1| 2| 3| 4| 5| 6

Before |12 |29 |16 |37 |28 |15

After |10| 25| 12| 32| 25| 12

(a) State the null hypothesis and alternative hypothesis

(b) Find the test statistic

(c) If the type-I error α = 0.1, find the critical value(s) and shade the rejection region(s)

(d) Base on the type-I error α and rejection region(s), given above, what is your conclusion?

A playground merry-go-round of radius ? = 2.0 m has a moment of inertia ? = 250 kg ⋅ m^2 is rotating at 15 rpm about a frictionless, vertical axle. Facing the axle, a 25-kg child hops onto the merry-goround and manages to sit down on the edge. (a) (10 pts) What is the total angular momentum of the ‘merry-go-round-child’ system before and after the child hops on the the merry-go-round? (b) (10 pts) What is the new angular speed, in rad/s, of the merry-go-round? (c) (5 pts) How many seconds will it take for the system to cover 5.0 complete revolutions? (d) (10 pts) What is the total kinetic energy of the system before and after the child hops on the the merry-go-round?

It is claimed that an industrial safety program is effective in reducing the loss of working hours due to factory accidents. The following data are collected concerning the weekly loss of working hours due to accidents in six plants both before and after the safety program is instituted. Do the data substantiate the claim ?

person 1 2 3 4 5 6

Before 12 29 16 37 28 15

After 10 25 12 32 25 12

(a) State the null hypothesis and alternative hypothesis

(b) Find the test statistic

(c) If the type-I error α = 0.1, find the critical value(s) and shade the rejection region(s)

(d) Base on the type-I error α and rejection region(s), given above, what is your conclusion?

1.) Ten men were selected to test an exercise device by using it 4 times per week for 30 minutes. Their resting pulse rates (beats per minute) were measured before the test began, and then again after 6 weeks. Assume the differences are approximately normally distributed.

a.) At significance level ? = .05, is there sufficient evidence to conclude that exercising in this way can reduce resting pulse rates?

b.) Give a 95% confidence interval for the mean difference. Interpret your interval in context.

Subject Before After

Allen 73 73

Brandon 83 79

Carlos 85 81

David 87 86

Erwin 91 86

Frank 98 91

George 87 84

Hans 85 83

Ivan 83 84

James 79 76

A weight loss program is announced by Health fitness centre claiming weight loss for sure. A random sample of eight recent participants showed the following weights before and after completing the course. At the 0.01 significance level, can we conclude the students lost weight?

(a) State the null hypothesis and the alternative hypothesis.

(b) What is the critical value of t?

(c) What is the computed value of t?

(d) Interpret the result. What is the p-value?

(e) What assumption needs to be made about the distribution of the differences?

7. Philip wants to take a speed-reading course, but his wife thinks that it is a waste of time. To convince her that the course will really change the way that he reads, Philip decides to conduct an informal study. He pols seven people, asking them to tell the number of pages they were able to read in an hour before and then after they took the course. The results he obtained are found in the following table. Construct and interpret a 95% confidence interval for the true mean increase in reading speeds for people who have taken the speed-reading course. Round your CI limits to 1 decimal place.

Number of pages read in one hour

Before Course: 35 50 45 50 60 70 65

After Course : 50 60 80 70 85 100 90

During the titration of a particular acid, the PH changes from 7.0 to 9.0 with the addition of 0.01mL of base. An indicator was used that had KI= 1.0x10-8. Calculate the ratio of basic to acidic forms of the indicators before and after the last 0.01mL of base was added. Use the result of your calculation to explain why this would or would not be a good indicator for this titration compared to phenolpthhalein.

a. I got PH change, then need to multply by 0.01ml of base. But why? What is that number called?

b. Need to calculate ratio of basic to acidic forms of the indicator before and after the last 0.01ml of base was added. I need precise steps of calculation with explainations.

c. How can I use my calculation to explain that the indicator used is good or bad for the experiment? Pleas explain.

The table below shows the number of hours per day 11 patients suffered from headaches before and after 7 weeks of soft tissue therapy. At α =​0.01, is there enough evidence to conclude that soft tissue therapy helps to reduce the length of time patients suffer from​ headaches? Assume the samples are random and​ dependent, and the population is normally distributed. USE THE CRITICAL REGION METHOD

Patient: 1 2 3 4 5 6 7 8 9 10 11

Daily Headache HRS.( Before) 3.1 , 2.6 , 3.6 , 3.9, 1.8 , 3.3 , 3.8, 1.8 , 2.5, 3.9 , 1.6

Daily Headache HRS.(After) 1.8 , 1.8, 1.4 , 2.2, 1.2 , 2.4 ,3.0 ,1.3 , 1.6 , 1.3, 1.1

9.The following relations describe monthly demand and supply for a computer support service catering to small businesses.

Q_d= 3000 – 10P

Q_s= -1000 + 10P

What is the autarky price and quantity produced?

What is the Welfare of the country as a whole before trade? ________________

If the world Price is $250, is this country a net importer or exporter? _________

And by how much? _________

What is the welfare of the country after trade? ____________

What is the net gain from trade?

10. The following relations describes the demand and supply for good x..

Q_d= 100 – 20P

Q_s= 20 + 20P

What is the autarky price and quantity produced?

What is the Welfare of the country as a whole before trade?

If the world Price is $1, is this country a net importer or exporter?

And by how much?

What is the welfare of the country after trade?

What is the net gain from trade? __________

five individuals with high blood pressure were given a new drug to see if it would lower their blood pressure. systolic blood pressure was measured before and after treatment for each individual. the results are below.

before: person 1= 170 person 2= 164 person 3= 168 person 4= 158 person 5= 183

after: person 1= 145 person 2= 132 person 3= 129 perosn 4= 135 perosn 5= 145

construct a 95% confidence interval for mean reduction in systolic blood pressure, round to one decimal place.

perform a hypothesis test at a 0.05 level on significance to determine if treatment for each individual. what is the pvalue round to the fourth decimal place.

do you reject the null, fail to reject the null or accept the null.