Discuss the concept of researcher bias. What are some ways a researcher might address these issues?

Using the language R

Generate five random data sets that follow the normal random distribution with mean 5, variance 2. The sizes of these five data sets is 10, 100, 1000, 10000 and 100000. Draw the histogram, boxplot and QQ-plot (normal probability plot) of five data sets. Please make comments about these plots

An investigator wants to test whether exposure to secondhand smoke before 1 year of life is associated with development of childhood asthma (defined as asthma diagnosed before 5 years of age). Give two possible study designs and indicate the pros and cons of each. Then, provide your recommendation for the most efficient design.

Is there a relationship between confidence intervals and two-tailed hypothesis tests? Let c be the level of confidence used to construct a confidence interval from sample data. Let α be the level of significance for a two-tailed hypothesis test. The following statement applies to hypothesis tests of the mean.

For a two-tailed hypothesis test with level of significance α and null hypothesis H₀: μ = k, we reject H₀ whenever k falls outside the c = 1 − αconfidence interval for μ based on the sample data. When k falls within the c = 1 − α confidence interval, we do not reject H₀.

(A corresponding relationship between confidence intervals and two-tailed hypothesis tests also is valid for other parameters, such as p, μ₁ − μ₂, or p₁− p₂, which we will study later.) Whenever the value of k given in the null hypothesis falls outside the c = 1 − α confidence interval for the parameter, we reject H₀. For example, consider a two-tailed hypothesis test with α = 0.01 and

H₀: μ = 20        H₁: μ ≠ 20

A random sample of size 34 has a sample mean x = 23 from a population with standard deviation σ = 5.

(a) What is the value of c = 1 − α?


Construct a 1 − α confidence interval for μ from the sample data. (Round your answers to two decimal places.)

What is the value of μ given in the null hypothesis (i.e., what is k)?
k =  

Is this value in the confidence interval?

YesNo     

Do we reject or fail to reject H₀ based on this information?

We fail to reject the null hypothesis since μ = 20 is not contained in this interval.We fail to reject the null hypothesis since μ = 20 is contained in this interval.     We reject the null hypothesis since μ = 20 is not contained in this interval.We reject the null hypothesis since μ = 20 is contained in this interval.

(b) Using methods of this chapter, find the P-value for the hypothesis test. (Round your answer to four decimal places.)


Do we reject or fail to reject H₀?

We fail to reject the null hypothesis since there is insufficient evidence that μ differs from 20.We reject the null hypothesis since there is sufficient evidence that μ differs from 20.     We reject the null hypothesis since there is insufficient evidence that μ differs from 20.We fail to reject the null hypothesis since there is sufficient evidence that μ differs from 20.

Compare your result to that of part (a).

We rejected the null hypothesis in part (b) but failed to reject the null hypothesis in part (a).We rejected the null hypothesis in part (a) but failed to reject the null hypothesis in part (b).     These results are the same.

Body mass index (BMI) in children is approximately normally distributed with a mean of 24.5 and a standard deviation of 6.2. Answer the following questions: a) A BMI between 25 and 30 is considered overweight. What proportion of children are overweight? b) A BMI of 30 or more is considered obese. What proportion of children are obese? c) In a random sample of 10 children, what is the probability that their mean BMI exceeds 25?

(a) In the cost accounting literature, the sample regression coefficient corresponding to x_k is regarded as an estimate of the true marginal cost of output associated with the variable x_k. Find a point estimate of the true marginal cost associated with total machine hours per month. (Enter your answer to three decimal places.)

Also, find a 95% confidence interval estimate of the true marginal cost associated with total machine hours. (Round your answers to three decimal places.)

(b) Test the hypothesis that the true marginal cost of output associated with total production of paper is $1,000. (Hint: Realize that this is analogous to testing the regression coefficient for total production of paper is 1.0.) Use a 10% level of significance.

State the hypotheses to be tested.

a.H₀: β₁ ≠ 1.0
H_a: β₁ = 1.0

b.H₀: β₁ = 1.0
H_a: β₁ ≠ 1.0    

c.H₀: β₂ ≠ 1.0
H_a: β₂ = 1.0

d.H₀: β₀ = 1.0
H_a: β₀ ≠ 1.0

e.H₀: β₂ = 1.0
H_a: β₂ ≠ 1.0

(c)State the decision rule.

a.Reject H₀ if p < 0.10.
Do not reject H₀ if p ≥ 0.10.

b.Reject H₀ if p > 0.05.
Do not reject H₀ if p ≤ 0.05.    

c.Reject H₀ if p > 0.10.
Do not reject H₀ if p ≤ 0.10.

d.Reject H₀ if p < 0.05.
Do not reject H₀ if p ≥ 0.05.

(d)State your decision.

a.Reject the null hypothesis. The true marginal cost of output associated with total production of paper is not $1,000.

b.Reject the null hypothesis. The true marginal cost of output associated with total production of paper may be $1,000.    

c.Do not reject the null hypothesis. The true marginal cost of output associated with total production of paper may be $1,000.

d.Do not reject the null hypothesis. The true marginal cost of output associated with total production of paper is not $1,000.

Mini Practice Problem #11

For the data in the following matrix:

If you were to perform a factorial ANOVA, how would you answer the following questions.

What numbers are compared to evaluate the main effect for the treatment? If there was a significant treatment main effect, how would you interpret this finding?

What numbers are compared to evaluate the main effect for gender? If there was a significant gender main effect, how would you interpret this finding?

If there was a treatment x gender interaction effect, what numbers or further statistical analyses would you conduct to determine where differences existed?

Answer the following question

What are some of the advanced features for modeling available in Excel? Based on what many of you have already seen of Excel in CS105, are you surprised that Excel has so many capabilities? Do you use Excel for anything other than school work today?  

A researcher compares two compounds (1 and 2) used in the manufacture of car tires that are designed to reduce braking distances for SUVs equipped with the tires. SUVs equipped with tires using compound 1 have a mean braking distance of 79 feet and a standard deviation of 7.3 feet. SUVs equipped with tires using compound 2 have a mean braking distance of 86 feet and a standard deviation of 8.8 feet. Suppose that a sample of 79 braking tests are performed for each compound. Using these results, test the claim that the braking distance for SUVs equipped with tires using compound 1 is shorter than the braking distance when compound 2 is used. Let μ1 be the true mean braking distance corresponding to compound 1 and μ2 be the true mean braking distance corresponding to compound 2. Use the 0.1 level of significance.

Do we reject or refuse to reject the null hypothesis?

Maria and John have decided that once they live in a home, they want to have a pet. Maria prefers cats and John prefers dogs. They go to an animal shelter and find several pets that they would love to take home. There are 7 Siamese cats, 9 common cats, 4 German Shepherds, 2 Labrador Retrievers, and 6 mixed-breed dogs. Since they can’t decide, they place all the adoption cards in a container and draw one. Answer each of the following questions separately, showing all your work to reach each answer.

a. What is the probability that they select a cat?

b. What are the odds that they select a cat?

c. What is the probability that they select either a common cat or a mixed-breed dog?

d. What is the probability that they select a dog that it is not a Labrador Retriever?

Question 10 (1 point)

EU (European Union) countries report that 46% of their labour force is female. Statistics Canada wants to determine if the percentage of women in the Canadian labour force is the same.

Statistics Canada selects a random sample of 525 employment records, and find that 229 of the people are women. They want to test the null hypothesis that the Canadian labour force has the same proportion of women as in the EU against the alternative that it is not the same. What would be the appropriate test to run?

Question 10 options:

Question 11 (1 point)

EU (European Union) countries report that 46% of their labour force is female. Statistics Canada wants to determine if the percentage of women in the Canadian labour force is the same.

Statistics Canada selects a random sample of 525 employment records, and find that 229 of the people are women. They want to test (at the 5% significance level) the null hypothesis that the Canadian labour force has the same proportion of women as in the EU against the alternative that it is less than that in the EU. What formula would you use to calculate the test statistic?

Question 11 options:

Question 12 (1 point)

EU (European Union) countries report that 46% of their labour force is female. Statistics Canada wants to determine if the percentage of women in the Canadian labour force is the same.

Statistics Canada selects a random sample of 525 employment records, and find that 229 of the people are women. They want to test (at the 5% significance level) the null hypothesis that the Canadian labour force has the same proportion of women as in the EU against the alternative that it is less than that in the EU. What is the p-value associated with this hypothesis test?

Question 12 options:

Question 13 (1 point)

EU (European Union) countries report that 46% of their labour force is female. Statistics Canada wants to determine if the percentage of women in the Canadian labour force is the same.

Statistics Canada selects a random sample of 525 employment records, and find that 229 of the people are women. They want to test (at the 5% significance level) the null hypothesis that the Canadian labour force has the same proportion of women as in the EU against the alternative that it is less than that in the EU. What conclusion would you draw, based on your calculations?

Question 13 options:

As part of a study of wheat maturation, an agronomist selected a sample of wheat plants at random from a field plot. For each plant, the agronomist measured the moisture content from two locations: one from the central portion and one from the top portion of the wheat head. The agronomist hypothesizes that the central portion of the wheat head has more moisture than the top portion. What can the agronomist conclude with an α of 0.01? The moisture content data are below.

a) What is the appropriate test statistic?
---Select--- na z-test One-Sample t-test Independent-Samples t-test Related-Samples t-test

b)
Condition 1:
---Select--- wheat maturation ,moisture content ,wheat head ,central portion, top portion
Condition 2:
---Select--- wheat maturation moisture content wheat head central portion top portion

c) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value = ; test statistic =  
Decision:  ---Select--- Reject H0 or Fail to reject H0

d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[ , ]

e) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d =_____ ;   ---Select--- na trivial effect small effect medium effect large effect
r² =_______ ;   ---Select--- na trivial effect small effect medium effect large effect

f) Make an interpretation based on the results.

A.The central portion of the wheat head had significantly more moisture than the top portion.

B.The central portion of the wheat head had significantly less moisture than the top portion.    

C.There was no significant moisture difference between the central and top portion of the wheat head.

PROBABILITY DISTRIBUTIONS

In a traffic study of a street in Ipswich, QLD, the following information was gathered.

- Cars passed by at an average rate of 300 cars per hour.

- The speed of the cars was normally distributed, with an average speed of 58 km/h and a variance of 2 km²/h².

Based on this information, you are asked to solve the likelihoods of certain events happening. For each question clearly indicate the random variable and the distribution it follows, solve by hand and check your answer using MATLAB.

1. What is the probability that there is less than 10 seconds time difference between one car and the next?

2. What is the probability that more than 3 cars pass by in a minute?

3. The speed limit of the road is 60 km=h. What is the probability that a random car is speeding?

4. What is the probability that there are no speeding cars within a 10 minute period?

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 17 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is

x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.26 gram.(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to two decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

n is large

σ is known

normal distribution of weights

uniform distribution of weights

σ is unknown

(c) Interpret your results in the context of this problem.

The probability to the true average weight of Allen's hummingbirds is equal to the sample mean.

There is a 20% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.    

The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.

There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region. The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.06 for the mean weights of the hummingbirds. (Round up to the nearest whole number.) _______ hummingbirds

Research by Steelcase found the average worker get interrupted every 11 minutes and takes 23 minutes to get back on task. From a random sample of 200 workers, 168 said they are interrupted every 11 minutes by email, texts, alerts, etc. Find the 90% confidence interval of the population proportion of workers who are interrupted every 11 minutes.