2. The dietary intake of vitamin C for adults in New York is not normally distributed, but it has a mean of µ = 88.2 mg/day and standard deviation σ = 12.1 mg/day

(a) What is the probability that a randomly selected New York adult’s vitamin C intake is greater than 100 mg/day? Think carefully about this!

(b) What is the probability that a sample of 100 randomly selected New York adults will have a mean greater than 89 mg/day?

(c) What is the probability that a sample of 200 randomly selected New York adults will have a mean between 88 mg/day and 88.5 mg/day?

The manager of a paint supply store wants to estimate the actual amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer. The manufacturer’s specifications state that the standard deviation of the amount of paint is equal to 0.022 gallon. A random sample of 64 cans is selected, and the sample mean amount of paint per 1-gallon can is 0.988 gallon. a. Construct a 99% confidence interval estimate of the population mean amount of paint included in a 1-gallon can. b. On the basis of your results, do you think that the manager has a right to complain to the manufacturer? Why? c. Must you assume that the population amount of paint per can is normally distributed here? Explain. d. Construct a 95% confidence interval estimate. How does this change your answer to (b)?

1). Write the null and alternative hypothesis. Make sure you write the correct “formula” (H_o or H_a), noting whether it is directional or non-directional depending on whether the question calls for an increase/decrease or simply a change!

2). Tell me what would be a Type I AND a Type II Error for each example. When you explain the type I and type II error for each, make sure you tell me what the conclusion would be and what the reality would be in each scenario.

-You read an article online that suggests that the number of negative tweets posted online about the TV show Game of Thrones significantly increased during the 2019 season, as compared to the previous season. You decide to test this hypothesis.

a) Null H_o:

b) Alternative H_a:

c) Type I Error:

d) Type II Error:

You’re waiting for Caltrain. Suppose that the waiting times have a mean of 12 minutes and a standard deviation of 3 minutes. Use the Chebyshev inequality to answer each of the following questions:

a) What is the largest possible probability that you’ll end up waiting either less than 6 minutes or more than 18 minutes for the train?

b) What is the smallest possible probability that you’ll wait between 6 and 18 minutes for the train?

c) What is the smallest possible probability that you’ll wait between 3 and 21 minutes for the train?

d) What is the smallest possible probability that you’ll wait between 0 and 24 minutes for the train?

e) Based on your answer to part (d), what is the largest possible probability that you’ll need to wait more than 24 minutes for the train? Why is this answer so dramatically different from your answer to #1c above?

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