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Please note that this question consists of four parts. You may use MINITAB to double check your final answer. However you MUST show all the mathematical work to get to the final answer. Just giving the answer without adequate work/explanation may result in zero for the question.   A study was conducted to determine the percentage of adults in United States who are afraid to fly. Of the 1075 adults in United States surveyed, 292 were afraid to fly. Give a point estimate for the true proportion of adults in United States who are afraid to fly. The study wants to release an interval estimate for the true proportion of adults in United States who are afraid to fly. What are the conditions that need to be satisfied in order to calculate a confidence interval? Are they satisfied?  Calculate a 95% confidence interval for the true proportion of adults in United States who are afraid to fly. Interpret the interval calculated in part 3. 

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. [fill1] 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.  

For each of the following, select the correct answer from the dropdown menu.  If A and B are independent events then P(A) = P(B). This is a [fill1] statement.  If A and B are mutually exclusive events, then

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:

Let A and B be events such that  Then P( A and B) is given by:

The average age of residents in a large residential retirement community is 69 years with standard deviation 5.8 years. A simple random sample of 100 residents is to be selected, and the sample mean age

Please note that this question consists of five parts. Show all your work. Just giving the answer without showing work may result in zero for the question.  A researcher claims that more than 24% of the adults in United States are afraid to fly. You want to test this claim. You find that in a random sample of 1075 adults in USA, 292 re afraid to fly. (You may use below provided MINITAB output to answer the following questions) Write the null and alternative hypotheses you would formulate to test the researchers claim. Check any conditions that need to be satisfied in order for you to continue with the above stated hypothesis test. What are the test statistic and the p value for the hypotheses you stated in part 1? Write your final conclusion in the context of this problem (You may use 5% significance level). Based on your conclusion in part 4, is it possible that you made an error? If so what error would that be?   

State whether below statement is either a True or a False statement. If it is false explain why. Please note that you can say something is true if it’s always true. A medical researcher is conducting an experiment to compare the frequencies of occurrences of side effects to treatment by a new drug for two groups of patients, those who had prior treatment and those who had not.  Researchers want to know if there is evidence that patients who have no prior treatment are more likely to have side effect.  The chi-square test for independence is appropriate for this research question.  

Here are copies of Z-table and T-table.  Z table.pdf T_table.pdf