Below pie chart summarizes the sources of energy in the United States and their corresponding percentages:  How many variables are summarized in this pie chart? What percentage of the sources of energy in the United States are from either Renewable Energy or Nuclear? What percentage of the sources of energy in the United States are other than Coal? If 1000 sources of energy were randomly chosen, what is the expected number from Petroleum?

Please note that this question consists of three parts. Show all your work/explanation. Just giving the answer without adequate work/explanation may result in zero for the question.  In a used car dealership that post cars for sale, 85% of the cars have automatic transmission, 20% are all-wheel drive and 15% have both features. For a randomly chosen car from this website: Are having these two features:  “automatic transmission” and “all-wheel drive” mutually exclusive? Explain your answer.  What is the probability that it has neither features? What is the probability of having the feature of “all-wheel drive”, if it has “automatic transmission”? 

Using the following five-number summary, indicate whether each statement below is true or false.  Minimum Q1 Median Q3 Maximum 18 36.5 55 72.9 99  

In a Statistics class, about 5% of the students received an “A” (93 or above) in the course. In this setting, the value “93” is known as:

Status of a faculty was coded as 1 if the faculty is Full Time and coded as 0 if the faculty is Part Time. The variable Status is: 

A student organization wanted to study voting preferences in its student body during the 2024 presidential election. They selected 150 students at random from each class, freshmen through seniors. The sampling technique being used is:  

State whether below statements are either a True or a False statement.  If a 99% confidence interval for the difference of two independent means is (-3.2, 10.4), then the two-sided test of the null hypothesis of no difference will be rejected at a 1% significance level. Sampling distribution of sample mean would be approximately normal with the same mean as the population mean

Please note that this question consists of seven parts. Use the MINITAB outputs provided to you to answer the question. Show all your work/explanation. Just giving the answer without adequate explanation/work may result in zero for the question.  A random sample of 15 students was collected by a researcher to investigate the relationship between a student’s emotional stability score (EmStability, X) and the student’s score on an achievement test (Achievement, Y). The researcher is interested in developing a regression model to predict the achievement (Achievement) based on the emotional stability (EmStability) using these data. Partial output of the regression analysis is provided below: Write the equation of the least squares regression line for predicting the Achievement based on the EmStability.  The researcher is interested in testing if the Achievement increases with increment in the EmStability. Write the appropriate null and alternative hypothesis you would formulate to answer this question. Use the proper notations when setting up the H_0 and H_a.  Calculate the test statistic. What is the degrees of freedom of distribution for the test statistic you calculated in part 3?  Calculate the p-value. You may use the table or MINITAB to find the final p value; however, you need to write the probability statement for the p-value for this test.  Write the final conclusion in the context of the problem. Use 5% significance level.  What is the predicted Achievement score when the EmStability is 19? Clearly show your work.  

A local furniture store found from the past observation that 25% of the people who enter the store actually buy something. Four potential customers enter the store (you may assume they are random). Find the probability of at least one sale to the four customers.

A clinical researcher wants to see whether a new medicine will help reduce blood sugar level. She randomly selects 20 persons and assigns them to the new medicine (length of the program is three months). For each person she records their blood sugar level as they start the medicine and after they complete the program. To test whether mean reduction in blood sugar level is significant, we would do: