1. You are a teacher and want to analyze if your morning class has significantly different scores than your afternoon class. You have 12 students in both of your classes. Compute a t-test for independent samples on these scores from the last quiz you administered and then use the eight steps to test the null hypothesis that there is no difference between the two conditions. Do the two groups differ?
Morning class Afternoon class
87 86
98 73
75 79
88 56
76 72
85 70
92 87
56 59
89 64
85 77
84 74
92 72

In our rental shop case, we know that on the busiest day we can expect 150 rentals, which forms the number of independent events or trials. We also know that, historically, 60% of our customers rent skis and 40% rent snowboards, which provides our probability. If we decide that we only need to have 65 snowboards in stock, what is the probability that we will run out of snowboard rentals on any specific day?

A New England Journal of Medicine study (November 1986) found that a substantial portion of acute hospital care is reported to be unnecessary. The physicians who conducted the study reviewed the medical records of 1,132 patients hospitalized at six different locations across the country. Overall, 60% of admissions in the sample were judged to be appropriate, 23% were deemed inappropriate, whereas 17% could have been avoided by the use of ambulatory surgery. Let p1, p2, and p3 represent the true percentages of hospital admissions in the three aforementioned categories: appropriate, inappropriate, and avoidable by ambulatory surgery, respectively. Using the techniques from categorical data analysis in a “one-way table”, answer the following questions:

(a) Construct 90% confidence intervals for p1, p2, and p3.

(b) Let H0 be the null hypothesis stating that p1=0.60, p2=0.25, p3=0.15. Formulate an appropriate alternative hypothesis Ha, and then test H0 using α =0.10.

The average income of 19 families who reside in a large metropolitan East Coast city is $62,245. The standard deviation is $9695. The average income of 12 families who reside in a rural area of the Midwest is $60,213, with a standard deviation of $2079. At α = 0.05, can it be concluded that the families who live in the cities have a higher income than those who live in the rural areas?

calculate test statistics and round to 2 decimal places

2. A clinical lab wants to evaluate the resistance power of its new medicine. It has provided the new medicine to a random sample of 300 rats and retained the old drug for the remaining (200 rats). Three months after the dosage of the new drug, the group with the new medicine has a resistance of 40.2 with a s.d of 6.5 while the group with the old drug had an average of 35 with a s.d of 4.5.

NOTE: Follow all the steps in hypothesis testing. You can use Graphpad for this one.

1. What is your Null and Alternate Hypothesis. (0.5 point)

2. Did the new medicine result in significantly higher resistance of the dogs? State the value of the test-statistic, the p-value and the 95% confidence interval. (1 point)

(c)What do you mean by saying that this is the confidence interval in this case? (0.5 point)

Conception about the hypothesis test.

Question: can the data be test by poission distribution

H0: it can be test by poission

H1: it cant be test by poission model

Final: we fail to reject H0.

My Question: My prof told me that even though we fail to reject H0, but it doesnt mean that H0 is trues.

therefore, what should I write on my conclusion. should I write "yes, it can be test by poission model???"

However, it doesn't mean it is true

Please follow the comment

Please make sure to display your thought process? It is imperative to be able to follow how the answer was deduced. Please be as thorough as possible. Please address all parts of this question.

A team of medical researchers wants to estimate the malaria infection rate in a difficult-to-access jungle region of [No Name Country]. There are 80 villages in the studied part of the jungle, which can be assumed to be rather similar to each other. Each village has at least 300 inhabitants. We want to test 200 individuals for malaria. Propose a cost-efficient sampling method using one or multiple (the one that applies the most" "PROBABILITY THEORY BASED MODELS" of Bernoulli, Binomial, Poisson distributions?

A real estate expert wanted to find the relationship between the sale price of houses and various characteristics of the houses. He collected data on five variables, recorded in the table, for 12 houses that were sold recently. The five variables arePrice: Sale price of a house in thousands of dollars. Lot Size: Size of the lot in acres. Living Area: Living area in square feet. Age: Age of a house in years. Type of house: town house (T) or Villa (V) Price Lot Size Living Area Age Type of house

Price 255 178 263 127 305 164 245 146 287 189 211 123

Lot Size1.4 0.9 1.8 0.7 2.6 1.2 2.1 1.1 2.8 1.6 1.7 0.5

Living area 2500 2250 2900 1800 3200 2400 2700 2050 2850 2600 2300 1700

Age 8 12 5 24 10 18 9 28 13 9 8 11

Type of the house T T T T T T T V V V V V

Find the regression equation for the town house e) Find the regression equation for the Villa f) What is the price of a town house with a lot size of 1.3, living area of 1800, and is 7 years old?

Before lending someone​ money, banks must decide whether they believe the applicant will repay the loan. One strategy used is a point system. Loan officers assess information about the​ applicant, totaling points they award for the​ person's income​ level, credit​ history, current debt​ burden, and so on. The higher the point​ total, the more convinced the bank is that​ it's safe to make the loan. Any applicant with a lower point total than a certain cutoff score is denied a loan. Think of this decision as a hypothesis test. Since the bank makes its profit from the interest collected on repaid​ loans, their null hypothesis is that the applicant will repay the loan and therefore should get the money. Only if the​ person's score falls below the minimum cutoff will the bank reject the null and deny the loan. Complete parts a through c below.

a) In this context, what is meant by the power of the test?

A. The power is the probability that the bank approves a loan that will be repaid.

B. The power is the probability that the bank denies a loan that would have been repaid.

C. The power is the probability that the bank approves a loan that will not be repaid.

D. The power is the probability that the bank denies a loan that would not have been repaid.

b) What could the bank do to increase the power?

A. The bank could hire additional loan officers to assess each​ applicant's information.

B. The bank could lower the cutoff score.

C. The bank could raise the cutoff score.

D. The bank could scrap the point system.

c) What is the disadvantage of taking the action in part b)?

A. A larger number of untrustworthy people would have their loans​ approved, and the bank would lose money from those unpaid loans.

B. The bank would have to spend more money on the additional loan officers.

C. The bank would have to spend additional time and money developing a new system.

D. A larger number of trustworthy people would be denied​ credit, and the bank would miss the opportunity to collect interest on those loans.

The housing market has recovered slowly from the economic crisis of 2008. Recently, in one large community, realtors randomly sampled 30 bids from potential buyers to estimate the average loss in home value. The sample showed the average loss was $9008 with a standard deviation of $1909. Complete parts (a) through (c) below.

a) What assumptions and conditions must be checked before finding a confidence interval? How would one check them?

A. The data are assumed to be dependent and to have a sample size that is large enough to have a sampling distribution that is approximately Normal. Check the independence assumption by ensuring that there are at least 10​ "successes" and 10​ "failures."

B. The data are assumed to be independent and from a Normal population. Check the independence assumption with the Nearly Normal Condition using a histogram. Check the Normal population assumption with the Randomization Condition.

C. The data are assumed to be independent and to have a sample size that is large enough to have a sampling distribution that is approximately Normal. Check the independence assumption with the Randomization Condition. Check the sample size assumption by ensuring that there are at least 10​ "successes" and 10​ "failures."

D. The data are assumed to be independent and from a Normal population. Check the independence assumption with the Randomization Condition. Check the Normal population assumption with the Nearly Normal Condition using a histogram.

b) Find a 90% confidence interval for the mean loss in value per home.

($___, $___)

(Round to the nearest whole number as needed.)

c) Interpret this interval and explain what 90% confidence means in this context. Choose the correct answer below.

A. One is 90​% confident that the true average loss in home value is between the lower boundary of the interval and the upper boundary of the interval.

B. There is a 90​% chance that the average true loss in home value is between the lower boundary of the interval and the upper boundary of the interval.

C. There is a 90​% chance that the true average loss in home value of the homes sampled is between the lower boundary of the interval and the upper boundary of the interval.

D. One is 90​% confident that the true average loss in home value of the homes sampled is between the lower boundary of the interval and the upper boundary of the interval.

Each Sunday I go to a bakery shop to buy a dozen (12) bread. Beginning on that Sunday and continuing through the following Saturday (7 days) I consume either 1 or 2 of the bread each day. Today, Sunday, I find that the bakery mistakenly gave me only 11 bread. In how many ways may I consume all of the bread I got this week? (For example, I might eat 2 today, 1 tomorrow, etc.)

Which of the following statement about charts is true?

The more data ink, the better

Data ink can sometimes help tell a richer story

We should make as many grids as possible in a chart

A useless chart is called "chart junk"

Assume that adults have IQ scores that are normally distributed with a mean of 95.8 and a standard deviation of 22.4. Find the probability that a randomly selected adult has an IQ greater than 127.6. ​(Hint: Draw a​ graph.) The probability that a randomly selected adult from this group has an IQ greater than 127.6 is nothing. ​(Round to four decimal places as​ needed.)

Multiple Choice

Select the best answer from the available choices for each question.

1.   Three people are acting in a play. Character A has 50% of the lines, Character B has 40%, and Character C has 10%. Each person has a different probability of making a mistake on any line, independently: 0.03 for A, 0.07 for B, and 0.20 for C. Given that a mistake occurred, what is the probability that it was C’s line?

  
•   0.02
  
•   0.063
  
•   0.317
  
•   0.444
  
•   None of the above

2.   Which matches the conditions for using a Binomial approximation to the Hypergeometric?

  
•   N must be large and n must be small relative to N
  
•   The sampling must be done with replacement
  
•   n must be large and r/N must be small
  
•   Two or more of the above
  
•   None of the above

3.   Suppose the amount of data you use on your phone (in units of 100 MB) has a Poisson distribution with mean 8 per month. You pay $15 per month plus $3 per 100 MB of data. Find the standard deviation of a random month's phone bill.

•   6.245

•   8.485

•   9.327
  
•   72
  
•   None of the above

4.   The amount of time a user plays Animal Crossing has an Exponential distribution with mean 30 minutes. Given that the user has been playing for 1 hour, what is the probability they will still be playing half an hour later?

•   0.012

•   0.135

•   0.368

•   0.632

•   None of the above

5.   Which of the following 4 statements is FALSE?

  
•   If X~Y (i.e. X and Y have the same distribution), then they have a correlation of 1
  
•   If X and Y are independent, they have a correlation of 0

•   If X and Y have a correlation of 0, and Y and Z have a correlation of 1, then X and Z have correlation of 0

•   Correlation tells us the strength and direction of the linear relationship between two variables, whereas covariance only tells us the direction

•   Two or more of the above are false

6.   Which of the following 4 statements is TRUE?

•   If X and Y have a negative correlation, they are independent

•   If X and Y have a correlation of 0, they are independent

•   If X and Y have a positive correlation, and Y and Z have a positive correlation, then X and Z have positive correlation

•   If X = -0.5Y, then the correlation of X and Y is -1

•   Two or more of the above are true

7.   Which of the following 4 statements is FALSE?

  
•   The Normal distribution has mean, median, and mode all equal to μ   

•   A Normal random variable with a larger variance has a smaller maximum height of its pdf

•   Approximately 95% of the area under the Standard Normal pdf is between -1 and 1

•   The cdf F(x) of a Normal random variable is strictly increasing for all Real values of x

•   Two or more of the above are false

8.   The return on stock X has mean 5 and standard deviation 3. The return on stock Y has mean 8 and standard deviation 10. The standard deviation of an equal portfolio of the two stocks (that is, 0.5X + 0.5Y) is 24.25. What is the correlation between X and Y?

•   -0.2
  
•   0

•   0.2

•   0.4
  
•   None of the above

9.     Suppose the length in cm of a male soccer player's foot follows a Normal distribution with mean 30 and variance 25. Suppose the length in cm of a female soccer player's foot follows a Normal distribution with mean 26 and variance 16. A male and female soccer player are selected at random. What is the probability the female player has a longer foot than the male player?

•   0.09

•   0.27

•   0.33

•   0.73

•   0.91

10.   Independently of one another, a randomly surveyed individual can be a non-smoker, a light smoker, or a heavy smoker with probabilities 60%, 30% and 10%, respectively. Suppose we randomly survey a sample of 100 people. Given that 37 of them are light smokers, what is the expected number of heavy smokers?

•   6.3

•   9

•   27

•   54

•   None of the above

11.   The Princess Theatre has 280 seats. 200 tickets are sold for the new popular movie: The Attack of the Goose. Despite every attendee having an assigned seat, they all decide to sit in seats at random. Find the variance of the number of people sitting in their assigned seat. (Hint: use indicator variables)

•   0.712

•   0.714

•   5.246

•   11.704

•   None of the above

In 1975 the journal Environmental News reported that a number of communities in Boston showed elevated levels of lead in the drinking water supplies. Water testing was done on a random sample of 248 households in these areas of Boston and results showed that 20% of the households had lead levels that were above the U.S. Public Health Service standard of 50 ppm. A nearby area that used anti-corrosives in its water supply as a preventative measure to reduce the leaching of lead from pipes into the water showed that 5% of 100 randomly selected households had lead levels in excess of the standard. Explain the approach you would use to evaluate whether there appeared to be an association (or difference in elevated lead levels) for the two communities. You don't have to do the calculation but must:

1. specify the null and alternative hypothesis

2. describe the statistical test or approach you would use

3. justify why you would use that test/approach.

4. identify the page in the text (or presentation & slide number) that contains the relevant equations.