A study was conducted to determine if taking a popularly advertised herbal supplement will result in weight loss in obese males. A random sample of clinically obese males was obtained. Each subject was weighed before taking the supplement and again after 60 days using the supplement. Subjects were told not to alter their diet in any way during the study period. The following table shows the observed results for the 6 subjects:

15. What are the appropriate hypotheses to use in this case to determine if the herbal supplement is effective in achieving weight loss in obese males?

To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.

1. At the 0.05 level of significance, the conclusion for this hypothesis test is:

n a test of the effectiveness of garlic for lowering​ cholesterol, 36 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes​ (before minus​ after) in their levels of LDL cholesterol​ (in mg/dL) have a mean of 0.1 and a standard deviation of 1.67 Use a 0.05 significance level to test the claim that with garlic​ treatment, the mean change in LDL cholesterol is greater than 00. What do the results suggest about the effectiveness of the garlic​ treatment? Assume that a simple random sample has been selected. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. H0​: muμ=00 ​mg/dL H1​: muμ>00 ​mg/dL

.Determine the test statistic.   .36

Determine the​ P-value. ???

For the following cases, you may use either the P-value approach or the rejection region approach to present a full hypothesis test, including:

1. Identifying the claim and H₀ and H_a,
2. Finding the appropriate standardized test statistic,
3. Finding the P-value or the rejection region,
4. Deciding whether to reject or fail to reject the null hypothesis, and
5. Interpreting the decision in the context of the original claim.

1. A scientist claims that pneumonia causes weight loss in mice.  The table below shows weight, in grams, of six mice before infection with pneumonia and two days after infection.  At α = 0.01, evaluate the scientist’s claim.

Before After

Mouse 1           19.8     18.4

Mouse 2           20.2     19.6

Mouse 3           19.9     19.1

Mouse 4           22.1     20.7

Mouse 5           23.4     22.2

Mouse 6           23.6     23.0

At a major food production facility, a cart of bananas with a mass of 200kg is at the top of a 10m high hill, moving with a speed of 6m/s. At the end of the production line is a segment where brakes are applied (uk = 0.4; D = 8m), and then the cart runs into a giant stopping spring (K = 10,000 N/m; total length = 4m).

a. Draw a FBD of the cart while in contact with the spring.

b. Show that the initial energy (at the top of the hill) of the cart is 23,200J.

c. Determine the distance the cart goes after touching the spring before it is brought to rest for the first time (answer to B is Eo).

d. Assuming that, after touching the spring, the cart travels 1.5m (not answer to part C) before stopping, determine the acceleration of the cart at the time its speed is zero.

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