) A researcher recruited 2100 men in his research and followed up every year for 4 years to find out the incidence rate of respiratory disease.

After 1 year, there was not a new diagnosis of respiratory disease, and 100 lost to follow up,

After 2 years, found one new case of respiratory disease and 99 lost to follow up,

After 3 years, found 7 new cases of respiratory diseases and seven hundred ninety three lost to follow up.

After 4 years, found eight new cases of respiratory diseases and three hundred ninety two lost to follow up.

Calculate the incidence rate of respiratory disease

(**new cases of respiratory disease and men lost to follow up were disease-free for six months) ** and contribute ½ years to the denominator)

As reported in "Runner's World" magazine, the times of the finishers in the New York City 10 km run are normally distributed with a mean of 61 minutes and a standard deviation of 9 minutes. Let x denote finishing time for the finishers.

a) The distribution of the variable x has mean____ and standard deviation____ .

b) The distribution of the standardized variable z has mean____ and standard deviation____ .

c) The percentage of finishers with times between 60 and 80 minutes is equal to the area under the standard normal curve between____ and____ .

d) The percentage of finishers with times exceeding 86 minutes is equal to the area under the standard normal curve that lies to the____ of____ .

1.The yearly salary (in thousands of dollars) for a small company are listed below. Find the mode, mean, median and population standard deviation and use the Empirical Rule to find a 95% confidence interval.

74 46 397 75 98 67 46 96

2. From the Measures of Central Tendencies computed above, which one would you use to represent the “average” company salary. Explain your reasoning.

Probability theory and the binomial expansion show that, were you to sample families consisting of four children 1/16 of these families would consist of 4 boys, 4/16 would consist of 3 boys and 1 girl, 6/16 would consist of 2 boys and 2 girls, 4/16 would consist of 1 boy and 3 girls, and 1/16 would consist of 4 girls. Do the data in the sample given in the next table approximate this expectation? Complete the table, calculate X², and answer the questions based on your calculations.

A. interpret this X² value, you have __________ degrees of freedom.

b. In this case do you accept/reject the hypothesis that these data approximate a dihybrid test cross ratio with independent assortment?a. In interpreting this X² value, you have _____ dregrees of freedom.

c. What is the probability that the deviations are due to chance alone?

D. Determine whether the overall ratio of boys to girls in the above data is consistent with the hypothesis of a 50:50 sex ratio. Remember that each family included in the table consists of four children; for example, 235 families consisted of 4 boys, 898 families consisted of 3 boys and 1 girl, and 1317 families consisted of 2 boys and 2 girls. Calculate X² for these data by completing the following table:

E. Accept/Reject ________; df=_____________; P=___________

F. Calculate the ratio of boys to girls; record here:

G. How have biologists explained sex ratio data such as those observed in this problem?

Please explain the steps...... Thanks

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for Vanguard Total Stock Index (all stocks). Let y be a random variable representing annual return for Vanguard Balanced Index (60% stock and 40% bond). For the past several years, we have the following data.

(a) Compute Σx, Σx², Σy, Σy².

(b) Use the results of part (a) to compute the sample mean, variance, and standard deviation for x and for y. (Round your answers to two decimal places.)

(c) Compute a 75% Chebyshev interval around the mean for x values and also for y values. (Round your answers to two decimal places.)

Use the intervals to compare the two funds.

75% of the returns for the balanced fund fall within a narrower range than those of the stock fund.75% of the returns for the stock fund fall within a narrower range than those of the balanced fund.    25% of the returns for the balanced fund fall within a narrower range than those of the stock fund.25% of the returns for the stock fund fall within a wider range than those of the balanced fund.

A population proportion is 0.4. A sample of size 200 will be taken and the sample proportion p-- will be used to estimate the population proportion. Use z-table.

Round your answers to four decimal places. Do not round intermediate calculations.

a. What is the probability that the sample proportion will be within +/- 0.03 of the population proportion?

b. What is the probability that the sample proportion will be within +/- 0.05 of the population proportion?

MUST INCLUDE:

The knowns

Graphs

Formulas

Steps to Solve

Box the answer

A simple random sample of 400 individuals provides 100 Yes responses.

a. What is the point estimate of the proportion of the population that would provide Yes responses? (to 2 decimals)

later use p-- rounded to 2 decimal places

b. What is your estimate of the standard of error of the proportion? ( to 4 decimals)

c. Compute the 95% confidence interval for the population proportion. (to 4 decimals)

MUST INCLUDE:

The knowns

Graphs

Formulas

Steps to Solve

Box the Answer

Wayne Collier designed an experiment to measure the
fuel efficiency of his family car under different tire pressures.
For each run, he set the tire pressure and then measured the
miles he drove on a highway (I-95 between Mills River and
Pisgah Forest, NC) until he ran out of fuel using 2 liters of fuel
each time. To do this, he made some alterations to the normal
flow of gasoline to the engine. In Wayne’s words, “I inserted
a T-junction into the fuel line just before the fuel filter, and a
line into the passenger compartment of my car, where it joined
with a graduated 2 liter Rubbermaid© bottle that I mounted in
d©
a box where the passenger seat is normally fastened. Then I
sealed off the fuel-return line, which under normal operation
sends excess fuel from the fuel pump back to the fuel tank.”
Suppose that you call the mean miles that he can drive with
µ.
µ
normal pressure in the tires
An unbiased estimate for
is the
mean of the sample runs, x. But Wayne has a different idea. He
decides to use the following estimator: He flips a fair coin. If the
coin comes up heads, he will add five miles to each observation.
If tails come up, he will subtract five miles from each observation.
(a) Show that Wayne’s estimate is, in fact, unbiased.
(b) Compare the standard deviation of Wayne’s estimate with
the standard deviation of the sample mean.
(c) Given your answer to (b), why does Wayne’s estimate not
make good sense scientifically

Question 1:

Some people are more susceptible to hypnosis than others. People who are highly suggestible have a vivid imagination and fantasy life. This has led researchers to hypothesize that the ability to recall dreams will also be affected by hypnotic susceptibility (HS). Dr. Flowers wanted to test this hypothesis. Using the Stanford Scale of Hypnotic Susceptibility, she assigned participants to low, medium, and high susceptibility groups. Dr. Flowers asked all participants to keep a dream diary. At the end of 1 month, the diaries were collected and Dr. Flowers counted the number of dreams each person had recalled.

What is the alternative research hypothesis for this study?

What is the null research hypothesis for this study?

What is the first word in the alternative statistical hypothesis for any experiment with three levels of a single IV?

What is the null statistical hypothesis for the study of dream recall among groups with different levels of hypnotic susceptibility?

μlowHS = μmedHS = μhighHSμlowHS = μmedHS = μhighHS

μlowHS ≠ μmedHS ≠ μhighHSμlowHS ≠ μmedHS ≠ μhighHS

In SPSS, analyze the data in the table using a one-way ANOVA.

Use the results in the output box labeled Descriptives to complete the following chart, which you will then use to answer the following 6 questions.

What is the mean of the low HS group? (2 decimal places)

What is the mean of the medium HS group? (2 decimal places)

What is the mean of the high HS group? (2 decimal places)

What is the SD of the low HS group? (2 decimal places)

What is the SD of the medium HS group? (2 decimal places)

What is the SD of the high HS group? (2 decimal places)

Using the results in the output box labeled ANOVA, answer the next two questions.

What is the F ratio reported in the source table? (2 decimal places)

What is the p value reported in the source table? (located in the column labeled Sig)(3 decimal places)

In SPSS, conduct a post hoc test using Tukey's HSD to determine which groups differ significantly.

Complete the chart below to help you answer the following 6 questions.

What is the absolute value of the mean difference between the low and the mediumhypnotic susceptibility conditions? (2 decimal places)

What is the absolute value of the mean difference between the low and the high hypnotic susceptibility conditions? (2 decimal places)

What is the absolute value of the mean difference between the medium and the high hypnotic susceptibility conditions? (2 decimal places)

What is the p value for the comparison between the low and the medium hypnotic susceptibility conditions? (3 decimal places)

What is the p value for the comparison between the low and the high hypnotic susceptibility conditions? (3 decimal places)

What is the p value for the comparison between the medium and the high hypnotic susceptibility conditions? (3 decimal places)

What are the F-obtained values?

What are the between-groups MS? (3 decimal places)

What are the within-groups MS? (3 decimal places)

What are the significance levels?

Which component of the F ratio is affected by the distance between the mean?

Which component of the F ratio is affected by the amount of variability within the group?

Which component of the F ratio is affected by the amount of variability within the group?

Write a complete APA-style conclusion.

This is a template you will use to report the results of Experiment 1 of this study in the same format in which you would write the Results section of an APA-style lab report or journal article:

Based on a one-way ANOVA conducted in SPSS (Version 25), hypnotic susceptibility (HS) does /does not have an effect on the number of dreams recalled, F(#,##) = ###, p= ###. Tukey’s post hoc tests revealed that fewer / the same number of / more dreams are recalled in the high HS condition (M= ###) than / as in the low HS condition (M= ###), p= ###. There is a / no significant difference between the number of dreams recalled in the low HS condition and the medium HS condition (M= ###), p= ###. There is also a / no significant difference between the number of dreams recalled in the medium HS condition and the high HS condition, p= ###. Therefore, the results confirm that high HS is associated with fewer / the same number of / more dreams being recalled when compared to those with low HS.

Suppose that the fuel price at a specific gas station consists of :

A fixed government fuel excise of $0.416/L

Wholesale costs for supplier, which average $0.712/L, with a variance of 0.10.

Retail costs (including profit margin) at an average of $0.212/L, with a variance of 0.0012.

a) Find the average total fuel cost on any given day

b) Given that wholesale and retail costs have a correlation of 0.7, find the variance in total fuel price

c) Assuming that the total fuel price is normally distributed, what is the probability of fuel being priced at less than $1/L on any given day?

A sample of 30 diabetic women was taken at a health center, and the age at which the disease appeared was recorded, as shown in the table

Get the following probability distribution

Agree or disagree with each of the following statements and provide a short explanation.

Arnold wanted to compare the effects of cardio exercise and weightlifting on weight loss. He ran the following two regressions on the same sample,

weightloss on 1; cardio

weightloss on 1; lifting

He found that the coefficient from the first regression was larger than the coefficient from the second regression and therefore concluded that all else equal, an additional hour of cardio leads to more weight loss than an additional hour of lifting.

wo men, A and B, who usually commute to work together decide to conduct an experiment to see whether one route is faster than the other. The men feel that their driving habits are approximately the same, so each morning for two weeks one driver is assigned to route I and the other to route II. The times, recorded to the nearest minute, are shown in the following table. Using this data, find the 98%98%confidence interval for the true mean difference between the average travel time for route I and the average travel time for route II.

Let d=(route I travel time)−(route II travel time)d=(route I travel time)−(route II travel time). Assume that the populations of travel times are normally distributed for both routes.

Step 1 of 4: Find the mean of the paired differences, d‾‾. Round your answer to one decimal place.

Step 2 of 4: Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Step 3 of 4: Find the standard deviation of the paired differences to be used in constructing the confidence interval. Round your answer to one decimal place.

Step 4 of 4: Construct the 98% confidence interval. Round your answers to one decimal place.

....lower endpoint...upper endpoint

The World Health Organization (WHO) keeps track of how many incidents of leprosy there are in the world. Using the WHO regions and the World Banks income groups, onc can sask if an income level and a WHO region are dependent on each other in terms of predicting where the disease is. Data on leprosy cases in different countries was collected for hte year 2011 and a summary is present in the following table.

1. Two-Way Table of Leprosy Cases:

1. Compute the probability that a person with leprosy is from the Americas. Show your work below:
2. Compute the probability that a person with leprosy lives from a high-income country. Show your work below:
3. Compute the probability that a person with leprosy is from the Americas and a high-income country. Show your work below:
4. Compute the probability that a person with leprosy is from a high-income country, given they are from the Americas. Show your work below:
5. Compute the probability that a person with leprosy is from a low-income country. Show your work below:
6. Compute the probability that a person with leprosy is from Africa. Show your work below:
7. Compute the probability that a person with leprosy is from Africa and a low-income country. Show your work below:
8. Compute the probability that a person with leprosy is from Africa, given they are from a low-income country. Show your work below:
9. Are the events that a person with leprosy is from Africa and Low-income country independent events? Why or why not? Explain below:
10. Are the events that a person with leprosy is from the Americas and high-income country independent events? Why or why not? Explain below:

In how many ways can 2 men, 4 women, 3 boys, and 3 girls be selected from 6 men, 8 women, 4 boys and 5 girls if a particular man and woman must be selected?