test was conducted to determine the effectiveness of using an anti-inflammatory cream on delayed-onset muscle soreness. A random sample of ten patients was treated with the cream on one arm and with a placebo on the other (control) arm. After four days, a measure of muscle soreness was then taken for each patient on each arm. The results are: Patient 1 2 3 4 5 6 7 8 9 10 Control Arm 46 22 10 14 26 29 29 47 20 13 Treated Arm 2 32 30 3 14 32 2 39 18 2 At α=0.01 level of significance, would you say there is less soreness in the treated arm? Your discussion must include null and alternative hypotheses, check of assumptions (with appropriate plots), the value of the test statistic, the P-value, and your conclusion in the context of the data.

Suppose you conduct 10 significant tests and obtain the following p-values:

Test 1 2 3 4 5 6 7 8 9 10

p-value 0.001 0.030 0.002 0.006 0.040 0.003 0.010 0.100 0.020 0.004

• Which tests’ null hypotheses will you reject if you wish to control the family-wise error rate (FWER) at a significance level of 0.05?

• Which tests’ null hypotheses will you reject if you wish to control the false discovery rate (FDR) at a level of 0.05? Use the Benjamini-Hochberg method to answer this question by hand.

• Verify the results by using the related function in R

Evaluate the following IVs’ exclusion restriction. Come up with an example for each when the exclusion restriction is violated.

a. Impact of sexually transmitted disease prevalence on risky sex behaviors. Instrument: distance from your home to the origin of the AIDS virus

b. Impact of eating breakfast on infant health. Instrument: having a long work commute

c. Impact of adult depression on wages. Instrument: depression measured as a teenager

d. Impact of being a female science professor on whether women major in science. Instrument: The fraction of female instructors who teach in a particular semester.

Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advanced indication of illness such as gout leukemia or lymphoma. Over a period of months an adult Male patient has taken eight blood tests for uric acid. The sample mean concentration was 5.33 mg/dL . The distribution of uric acid in healthy adult Males can be assumed to be normal, with population standard deviation 1.85 mg/dL. In steps we are going to find a 95% confidence interval for the population mean.

1a. In order to find any confidence interval in the chapter, you must calculate the EBM ( error bound) value. In this case you must identify the critical value to be used for zCL.

b. What is the error bound for a population mean, EMB, for this problem.

c. What is the range from low to high for the population mean.

d. Interpret the confidence interval in the context of the problem.
I am 95% confident that.............

2. What is the critical value for a 99% confidence level when the sample size is 14 and s is known?

b. What is the critical value of 95% confidence level when the sample size is 44 and s is known?

Elevator ride: Engineers are designing a large elevator that will accommodate 43 people. The maximum weight the elevator can hold safely is 8643 pounds. According to the National Health Statistics Reports, the weights of adult U.S. men have mean 189 pounds and standard deviation 63 pounds, and the weights of adult U.S. women have mean 170 pounds and standard deviation 72 pounds. Use the TI-84 Plus calculator.

(a) If 43 people are on the elevator, and their total weight is 8643 pounds, what is their average weight?

(b) If a random sample of 43 adult men ride the elevator, what is the probability that the maximum safe weight will be exceeded? Round the answer to at least four decimal places

(c) If a random sample of 43 adult women ride the elevator, what is the probability that the maximum safe weight will be exceeded? Round the answer to at least four decimal places.

A sample of size 8 will be drawn from a normal population with mean 63 and standard deviation 12. Use the TI-84 Plus calculator.

(a) Is it appropriate to use the normal distribution to find probabilities for x bar?

(b) Find the probability that x bar will be between 53 and 73. Round the answer to at least four decimal places.

(c) Find the 83^rd percentile of x bar. Round the answer to at least two decimal places.

In a clinical study of an allergy drug, 109 of the 202 subjects reported experiencing significant relief from their symptoms. at the .01 significance level, test the claim that more than 50% of those using the drug experienced relief. what is the rejection rule?

Can you find and attach here an example of a statistically incorrect graph which has really been used/published somewhere? Explain why it is considered statistically incorrect.

1) The hypergeometric probability distribution is closely related to the binomial distribution except that the trials are not independent and the probability of success changes from trial to trial.

True/False

2) The stationarity assumption states that the probability of success in a given binomial distribution does not change from trial to trial.

True/False

3) It is possible for a discrete random variable to assume either a finite number of values or an infinite sequence of values.

True/False

4) Which distribution is used to calculate the probability of a given number of successes for a set number of trials where the only two options are success and failure?

A) The discrete - uniform distribution

B) A bivariate discrete distribution

C) The Poisson distribution

D) The binomial distribution

Research Question: Does the spatial ability differ by biological sex?
(Use Data A)

Null Hypothesis: Spatial ability does not differ by biological sex.

1. What is the statistic and its formula to address this research question? [1pt]

4. Calculate the t-value? [2 pt]

5. What is the critical value if alpha = 0.05 for two-tailed test? [2 pt]

6. Do we reject or accept the null hypothesis?  

7. What is the effect size (Cohen’s d)? [1 pt]

Data A: Students’ Spatial Ability

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

A random sample of medical files is used to estimate the proportion p of all people who have blood type B.

(a) If you have no preliminary estimate for p, how many medical files should you include in a random sample in order to be 85% sure that the point estimate p̂ will be within a distance of 0.03 from p? (Round your answer up to the nearest whole number.)
medical files

(b) Answer part (a) if you use the preliminary estimate that about 9 out of 90 people have blood type B.
medical files

1. What are the six steps of hypothesis testing?
2. What does it mean if we reject the null hypothesis?
3. How does statistical significance differ from practical significance?
4. What is the difference between a one-tailed and a two-tailed test? Why is a two-tailed test preferred over a one-tailed test?

Young and Company claims that its pressurized diving bell will, on average, maintain its integrity to depths of 2500 feet or more. You take a random sample of 50 of the bells. The average maximum depth for bells in your sample is 2455 feet. Set up an appropriate hypothesis test using Young and Company’s claim as the null hypothesis. Assume the population standard deviation is 200 feet. Use a 1% significance level.

a) What is the p-value that you calculate for this sample?

b) Can you reject the company's claim at the 1% level?

3) You are rolling a 12 sided die 8 times.

a) What is the size for the sample space? Write 3 different outcomes

Find the probability for the following

b) All of them are different

c) All of them are consecutive

d) Exactly four 9s and exactly five 12s

e) At least one 11