PLEASE MAKE SURE THE CONCLUSION IS CLEAR AND ANSWERS THE QUESTION DIRECTLY. Please show work so I can understand what your process was. I already have some answers but I just need to know if they are right

1. Bob is the owner of a home improvement store. He has hired you to check his machine's calibration prior to starting production on a large order. To check this, you set the machine to create 1.5 inch bolts and manufacture a random sample of 200 bolts. That sample of bolts has an average length of 1.521 inches with a standard deviation of 0.204 inches.

Does this sample provide convincing evidence that the machine is working properly or should it be shut down for repairs?

• I said "We will assume a 0.05 sig level for our conclusion. Since 0.147 > 0.05 we will fail to reject the null hypothesis meaning that we have enough evidence to show that the machines work as needed." Is this correct? If not please put the correct answer.

1. The annual tuition and parent rating of 12 private schools is shown on the scatterplot. The schools are rated on a scale of 0 to 100.

Scatterplot with x axis labeled Tuition Price, US dollars going from 0 to 12,000 and y axis labeled Rating going from 0 to 100. Values at 3,435, 40; 3,884, 76; 4,436, 32; 4,464, 23; 5,782, 86; 5,931, 22; 5,978, 37; 6,305, 76; 7,922, 36; 9,147, 80; 9,315, 4; 9,642, 55.

Part A: Describe the association shown in the scatterplot. (4 points).

Part B: Give an example of a data point that affects the appropriateness of using a linear regression model to fit all the data. Explain. (4 points)

Part C: Give an example of a school that is cost effective and rated highly by parents. (2 points) (10 points)

1. Two opposing opinions were shown to a random sample of 1,500 buyers of a particular political news app in the United States. The opinions, shown in a random order to each buyer, were as follows:

Opinion A: Improving the healthcare system is more important than improving the education system.

Opinion B: Improving the education system is more important than improving the healthcare system.

Buyers were to choose the opinion that most closely reflected their own. If they felt neutral on the topics, they were to choose a third option of "Neutral."

The outcomes were as follows:

39% chose Opinion A, 54% chose Opinion B, and 7% chose "Neutral."

Part A: Cre@te and interpret a 98% confidence interval for the proportion of all US buyers of this particular app who would have chosen Opinion B. (5 points)

Part B: The number of buyers that chose Opinion B and the number of buyers that did not choose Opinion B are both greater than 10. Why must this inference condition be met? (5 points) (10 points)

1. To increase sales, an online clothing store began giving a 50% off coupon to random customers. Customers didn't know whether they would receive the coupon until after the final sale. The website claimed that one in five customers received the coupon. Six customers each made purchases from the website. Let X = the number of customers that received the 50% off coupon.

Part A: Is X a binomial random variable? Explain. (3 points)

Part B: What is the mean and standard deviation of X? Provide an interpretation for each value in context. (4 points)

Part C: Two of the six customers receive the coupon with their purchase. Is the store's claim accurate? Compute P(X 2) and use the result to justify your answer. (3 points) (10 points)

1. In a study of the performance of a new engine design, the weight of 12 speed boats (in tons) and the top speed (in mph) were recorded. A regression line was generated and shown to be an appropriate description of the relationship. The results of the regression analysis are below.

Depend Variable: Top Speed

Variable: Constant Weight

Coefficient: 107.58 & 0.8710

s.e. of Coeff: 11.12 & 0.4146

t-ratio: 9.67 & 2.10

prob: 0.000 & 0.062o

R squared = 30.6% R squared (adjusted) = 23.7%

s = 10.42 with 12 - 2 = 10 degrees of freedom

Part A: What is the LSRL based on the analysis provided? Make sure to identify what the variables represent in the context of the problem. (4 points)

Part B: What is the predicted value for the top speed of a boat if its weight is 4 tons? Show your work. (6 points)