Give an example of a situation when you should perform a paired T-test and an example of when you should do an unpaired comparison.

7. A nutritionist wants to determine whether people who regularly drink one protein shake per day have different cholesterol levels than people in general. In the general population, cholesterol is normally distributed with μ = 190 and σ = 30. A person followed the protein shake regimen for two months and his cholesterol is 155. Use the 1% significance level to test the nutritionist’s idea.

1. Use the five steps of hypothesis testing. Explicitly label each of these five steps.
2. Draw a curve and label the cutoff(s), rejection region(s), and sample’s score.
3. Provide an interpretation of the finding.

Interpretation: One sentence conclusion of the hypothesis test that should be free of statistical jargon

8. A forensic psychologist studying a new type of polygraph (lie detector) test. On average, the older polygraph test is 75% accurate, with a standard deviation of 6.5%. With the new polygraph test, the operator correctly identified 83.5% of the false responses. Using the .05 level of significance, is the accuracy of the new polygraph better from the older one?

(a) Use the five steps of hypothesis testing. Explicitly label each of these five steps.

(b) Draw a curve and label the cutoff(s), rejection region(s), and sample’s score.

(c) Provide an interpretation of the finding.

Interpretation: One sentence conclusion of the hypothesis test that should be free of statistical jargon

The weight of a small Starbucks coffee is a normally distributed random variable with a mean of 385 grams and a standard deviation of 8 grams. Find the weight that corresponds to each event. (Use Excel or Appendix C to calculate the z-value. Round your final answers to 2 decimal places.) a. Highest 30 percent b. Middle 70 percent to c. Highest 90 percent d. Lowest 20 percent

For the following data sets, are the samples positively skewed, negatively skewed or approximately symmetric? (You can use R to justify your answer.) (a) A = {0.9961905,0.9493184,0.8332006,0.9513567,0.9856061,0.9136707,0.9706223, 0.6834221, 0.8527071, 0.8052218, 0.9798628, 0.9862662}. (b) B = {0.256907054,0.371948965,0.302661234,0.245459145,0.488603820,0.435416721, 0.203228122, 0.004436282, 0.115262446, 0.058988085, 0.256066243, 0.141507075}. (c) C = {0.139061819,0.025883617,0.096332657,0.115620817,0.274004925,0.059080122, 0.072580116, 0.008576388, 0.068673036, 0.379232748, 0.117313230, 0.086692960}.

The number of words in the active vocabulary of children of a particular age is normally distributed with a mean of 3000 and a standard deviation of 500.

Use the Normal Curve Table to determine the number of words a child needs to have in his/her vocabulary in order to be included

(a) among the top 5% of vocabulary scores

(b) among the top 20% of vocabulary scores

(c) among the bottom 10% of vocabulary scores

1. What is meant by a “null” hypothesis?
2. How do you test a null hypothesis?

what conclusion can be drawn from a study with a null result

DO NOT COPY AND PASTE FROM THE WEBSITE!!!! I NEED YOUR OWN WORD!!!

Explain the seeming contradiction in the One-Way ANOVA; namely, that the null hypothesis is about comparing the means of three or more populations, whereas the actual testing of means is about using ANOVA analysis to compare variances. Why is this so?

Referring back to the process map that I worked in class that involved “getting to work on time”. Suppose that during the construction of that process map, we came up with many potential causes for why we might be getting to work late. We placed those causes in a FMEA and one of the causes that had a high RPN was “getting to bed too late.” Up until that point, it was just a feeling that getting to bed late was causing us to get to work late. However, we decided to do an experiment. For 8 weeks (5 Days per week) we tried to go to bed earlier. For these 8 weeks, we recorded our arrival time at work. The following is the arrival times. Note: Our specification for arrival is 8:00 am, which is 480 minutes.) Using the same notation, we put the arrival times in minutes. The mean and standard deviation for the 40 arrival times above is 447.38 and 11.21, respectively, if you want to work the following two questions by hand.

1) Calculate the 95% confidence interval for the mean arrival time using the data above.

2) If our previous average arrival time was 452 minutes, did we significantly change the process of getting to work on time? Or in other words, is the arrival time different? Use your confidence interval from question 1 to answer this question.

3) If our previous average arrival time was 452 minutes, did we significantly change the process of getting to work on time? Or in other words, is the arrival time different? Perform a hypothesis test to answer this question at the 5% level of significance. (Use a t-statistic)

(1 point) Suppose a group of 1000 smokers (who all wanted to give up smoking) were randomly assigned to receive an antidepressant drug or a placebo for six weeks. Of the 184 patients who received the antidepressant drug, 39 were not smoking one year later. Of the 816 patients who received the placebo, 167 were not smoking one year later. Given the null hypothesis H0:(pdrug−pplacebo)=0 and the alternative hypothesis Ha:(pdrug−pplacebo)≠0, conduct a test to see if taking an antidepressant drug can help smokers stop smoking. Use α=0.01,

(a) The test statistic is ____

(b) The P-value is____

(c) The final conclusion is

A. There is not sufficient evidence to determine whether the antidepressant drug had an effect on changing smoking habits after one year.

B. There seems to be evidence that the patients taking the antidepressant drug have a different success rate of not smoking after one year than the placebo group.

Consider these 4 samples potentially drawn from 4 different populations. Sample #1) 25 19 14 21 18 18 19 19 Sample #2) 25 15 22 20 15 20 16 20 20 16 20 11 Sample #3) 22 16 23 13 14 19 18 10 11 Sample #4) 12 11 13 10 25 19 Test the hypothesis using the samples above.

Assuming that a = 0.05

Ho: u1 = u2

Ha: u1 not equal to u2

Ho: u2 < = u3

Ha: u2 > u3

Consider these 4 samples potentially drawn from 4 different populations. Sample #1) 25 19 14 21 18 18 19 19 Sample #2) 25 15 22 20 15 20 16 20 20 16 20 11 Sample #3) 22 16 23 13 14 19 18 10 11 Sample #4) 12 11 13 10 25 19 Test the hypothesis using the samples.

assuming that a = 0.05

Ho: u2 = u3

Ha: u2 not equal to u3

Ho: sigma 2 < = to sigma 3

Ha: sigma 2 > sigma 3

The average exam score for students enrolled in statistics classes at Indiana University Northwest is 80 and grades are normally distributed. A professor decides to select a random sample of 25 students from his CJ statistics class to see how CJ students compare to the student body in terms of exam performance. The average exam score of this sample is 78 with a variance equal to 100. Are the stats exam scores of the students in the CJ class significantly different when compared to the average university student at IUN?

a. Reach a statistical conclusion

b. Interpret your results

c. What would be your statistical conclusion and interpretation if the size of the selected sample would be 100?

2. Using the information provided at Q1, calculate the 95% confidence interval of the mean stats exam scores for the population of CJ students enrolled at IUN. [sample size = 25]

a. Interpret the 95%CI

b. Test the hypothesis that the CJ students’ population mean at stats exam is 80. Do you reject or fail to reject the null hypothesis? Justify your conclusion.

1. (13pt) The U.S. Census Bureau computes quarterly vacancy and homeownership rates by state and metropolitan statistical areas. The following data are the rental vacancy rates in percentage (%) grouped by region for the last quarter of 2018 using a sample of 4 statistical metropolitan areas.

                                     Vacancy rates (%)

1. (10pt) You are hired as statistician to test whether there are any differences among the regions regarding vacancy rates and you should allow for 10% error.

2. (3pt) Do you think that the mean vacancy rate is the same for these regions? Why?

A researcher wants to know how many security cameras are on average in stores located in a large shopping mall. He randomly selects a sample of 9 stores and finds that on average there are 2.7 security cameras per store with a standard deviation equal to 1.27.

a. Calculate and interpret the 95% confidence interval for the average number of security cameras per store

b. Test the hypothesis that the mean number of cameras per store is 4 at p = 05, 2-tail test. Justify your statistical conclusion.

c. Calculate and interpret the 90% confidence interval for the average number of security cameras per store