For hypothesis tests show the null and alternative hypothesis - the assignment of the claim, the distribution with the rejection and failure to reject regions, the p-value (if appropriate) the test statistic and the three-part conclusion.

b. For all other types of problems show all work and/or write down your calculator steps.

1. Why do statisticians use 95% as the level of confidence if none is given?Another way to think about this question is how does the empirical rule imply this level of confidence?

2. What is the default level of significance and how is this connected to the empirical rule?

3. Describe the levels of measurement.

4. Describe the similarities and the differences between stratified sampling and cluster sampling.

5. In a survey of U.S. adults who attend at least one concert a year found that 57% say concert tickets are too expensive. You randomly select 100 of these adults. Answer the following questions related to this scenario.

a. You are to use the normal approximation to a binomial distribution for this problem. There are two computations that are necessary in determining this process is supposed to be used. Show those formula and the resulting computations related to this problem.

b. What is the probability that at least 53 of these adults will say that concert tickets are too expensive? (show calculators steps)

c. What is the probability that less than 53 of these adults will say that concert tickets are too expensive? (Show your work on this or calculator steps)

6a. Suppose r=.65 and n=15. Would you conclude that you have correlation or no correlation?

b. Identify the critical value that is used to determine this and write it below.

c. What level of significance did you use?

7. Use the following data and compute the mean and the standard deviation by hand. Your data is from a population and the data set is:1,2,3

You can do either number 8a or number 8b but do not do both

8a Find the minimum sample size for the following. You wish to estimate with 90%

confidence and within 15% of the true population, the proportion of senior citizens that need to be treated for heart disease. There is no initial estimate for p-hat (Hint: think half and half).

8b. A sample of 45 swimmers had a mean time for the 50m fly of 25.23 seconds with a standard deviation of 1.4 seconds. Construct the confidenceinterval for the mean time on the 50m fly.Remember to state the calculator steps.

9. In problem number 7, what would you have divided by for the standard deviation if you were told it was a sample?

10. This must be done by hand but you can use the calculator for computations - Find the mean of the following frequency table.

class	frequency
10-19	1
20-29	8
30-39	9
40-49	7

11 The time a person feels ill from covid-19 is normally distributed with a mean of 13 days and a population standard deviation of 2 days (fake data by the way). If 36 people who have covid-19 are randomly selected, find the probability that they have a mean time in days of feeling ill is more than 13.5 days.

12. In number 11 it is not necessary to state that the population is normally distributed. How can you tell that the statement about normality is not necessary?

13. a. Generate the sample space for the following binomial situation. You will roll the die two times - total. The die has two colors on it. Two of the sides are red and four of the sides are blue. You consider a "success" rolling a red (red side is facing up).The blue sides are considered failures.

13. b. Generate the probability distribution where x is the number of times you rolled a red (Hint:the probability of success on one roll is 2/6 or 1/3).

x	0	1	2
P(x)

13. c. What is the mean and the standard deviation? (Hint:There are actually two ways to determine these but the quick way is to recognize that this is a binomial distribution).

	Dogs - yes	Dogs - no	Total
Cat - yes	7	23	30
Cat - no	10	16	26
Total	17	39	56

Use the table above to answer problems number 14, 15 and 16. Fifty-six people were asked two questions. They were asked if they have a cat and if they have a dog. They could answer yes or no to both questions.

14. What is the probability of getting a person who says they do not have a cat and they do not have a dog?

15. What is the probability of getting a person who says no to having a cat given they said yes they have a dog?

16. Show the computations behind this (this is not a hypothesis test): Are the events of having a dog and having a cat independent or dependent (causal not relational)?

goodness of fit

17. This is the one hypothesis test that must be done by hand -please note that no p-value will be generated: The loons are trying to determine the percent of box seats, regular seats and grass seats filled on any game. The people in the ticket office claim that 10% of all seats will be box seats, 35% will be regular seats and 55% will be grass seats. They did a count on the last game and found that out of 5000 people who attended 400 were in box seats, 3600 were in regular seats and 1000 were in grass seats. Is there enough evidence to support the claim made by the ticket office?

You are to do either 18 or 19 but not both

proportion

18. A medical researcher is conducting a study to test the effect of an anti-depression drug. At the end of the study, the researcher found that of the 400 randomly selected subjects who took the drug 201 had no improvement at all. Of the 700 randomly selected subjects who took the placebo 307 had no improvement at all. At the level of significance of .05,can you support the claim that the proportion of subjects that have no improvement is the same for both groups?

mean

19. A random sample of 144 medical school applicants at a university has a mean total score of 706 on the MCAT. According to a report the mean score for the school's applicants is more than 710. Assume the population standard deviation is 15. At the level of significance .10, is there enough evidence to refute the report's claim.

You are to do 20 or 21 but not both

ANOVA

20. The education community is concerned about students not getting the right amount of calories per day (as recommended by age/weight etc) . A researcher does a study of many local schools. The table shows the number of students who got the correct number of calories per day in each school by grade. Can you conclude that the numbers of students who got the correct number of calories is the same for all grades? Test the claim at the level of significance of .05.

Grade 9	Grade 10	Grade 11	Grade 12
34	48	69	70
45	31	59	36
34	49	45	68
40	46	36	55
61	37	31
13

Independence

21. You are investigating the relationship between the ages of U.S. adults and what aspect of career development they consider to be the most important. You randomly collect the data shown in the contingency table. Is there enough evidence to conclude that the age is related to which aspect of career development is considered to be the most important?

Age	Learning new skills	Pay increases	Career path
18-26 years	6	10	9
27-41 years	14	17	3
42-65	2	1	12

22. You go to a fancy restaurant and you see there are 4 salad/appetizer options, 3 entre options and 7 desert options. You are to select 2 salad/appetizers, 1 entre and 2 deserts. How many possible meals could result?

Correlation

23. A researcher wants to determine if there is a linear relationship between age and height. The following table represents the data collected. 1.) Display the data in a scatter plot on your calculator, draw a quick sketch below. 2.) Then find the linear regression and put the line of best fit on the sketch - making sure to state the linear regression equation. 3.) Also, state the value for the correlation coefficient and determine if this is significant correlation or no correlation using the table in the back of the book. 4.) Please state the critical value you found from the table.

Age in years	8	15	45	32	66	75	81	55	45
Height in feet	3	5.7	5.5	5.2	6	5.2	5.1	5.9	5.8

Means

24. There are two math teachers at Delta College who are at odds about pedagogy. One teacher (teacher A) claims that the traditional way of teaching math is better. Teacher A's students had a mean score of 77 with a standard deviation of 6. This teacher had 20 students take the placement test. Teacher B's students had a mean score of 83 with a standard deviation of 3. This teacher had 10 students take the test. Can you support the claim that the traditional way of teaching math is better? Assume that the populations are normal and that the variances are not equal.