Consider a sample with data values of 26, 24, 23, 18, 31, 35, 29, and 24. Compute the range, interquartile range, variance, and standard deviation

Suppose we have data from a health survey conducted in year 2000. Data were obtained from a random sample of 1000 persons.

An OLS linear regression analysis was carried out in the following way:

Dependent Variable: Systolic blood pressure (SBP, in mmHg)

Independent Variables: Gender (1 if female, 0 if male)

Age (in years)

Education (binary variables for “Not graduated from high school” and “Graduated from high school (but not from college)”; the reference category is “Graduated from college”)

A part of the results is shown below. The column labeled “Beta” show estimated values of partial regression coefficients. (It can be interpreted that beta’s for the reference categories, “Male” and “Graduated from college”, are fixed to be zero.) The p-values are for the two-sided test.

Variables	Beta	p-value
(Constant)	100.00	<0.01
Gender (Female)	-3.00	0.04
Age (in years)	0.50	<0.01
Education
Not graduated from high school	5.00	<0.01
Graduated from high school	2.00	0.08

1. According to the results of this regression analysis, how much expected difference in systolic blood pressure (in mmHg) is estimated:

1-1. between the two education categories, “Not graduated from high school” and “Graduated from college”, controlling for gender and age (i.e., among those who have the same gender and at the same age)?

1-2. between males and females, controlling for age and education?

2. Suppose we change the reference category of education from “Graduated from college” to “Graduated from high school” and do the same regression analysis again.

What will be the value of partial regression coefficient (beta) for “Not graduated from high school”?

(Hint: The expected SBP differences among the education categories do not change.)

Choose a population that you would plan to sample or survey. Your discussion board thread title should be "Sampling from ______". Some ideas for populations to take a sample from:

Mesa students

San Diego community college students

All San Diego college students

Adults in San Diego

Starbucks customers

Your choice!

Describe an perfect scenario sampling method: Describe in your own words one of the sampling methods learned in class and how it could be applied to your population - in this case, you can assume you will have access to things like a list of everyone living in San Diego.

Describe a realistic sampling method. Being that you don't actually have a list of all San Diego residents (or similar for your population), how would YOU go about trying to get a representative sample? No need to use any fancy terms or definitions here, just describe how you'd collect data from 100 people for your sample.

What are some limitations that will arise with your realistic scenario? Are there groups that might be left out?

Answer all of this in Approximately 150-200 words in length and well-written.

You manage an ice cream factory that makes two flavors: Creamy Vanilla and Continental Mocha. Into each quart of Creamy Vanilla go 2 eggs and 3 cups of cream. Into each quart of Continental Mocha go 1 egg and 3 cups of cream. You have in stock 500 eggs and 900 cups of cream. You make a profit of $3 on each quart of Creamy Vanilla and $2 on each quart of Continental Mocha. How many quarts of each flavor should you make to earn the largest profit?

In a lottery 5 different numbers are chosen from the first 90 positive integers.

(a) How many possible outcomes are there? (An outcome is an unordered sample of five numbers.)

(b) How many outcomes are there with the number 1 appearing among the five chosen numbers?

(c) How many outcomes are there with two numbers below 50 and three numbers above 60?

(d) How many outcomes are there with the property that the last digits of all five numbers are different? (The last digit of 5 is 5 and the last digit of 34 is 4.)

In an article in the Journal of Management, Joseph Martocchio studied and estimated the costs of employee absences. Assume an infinite population. The mean amount of paid time lost during a three-month period was 1.0 day per employee with a standard deviation of 1.4 days. The mean amount of unpaid time lost during a three month period was 1.2 days per employee with a standard deviation of 1.6 days. Suppose we randomly select a sample of 100 blue-collar workers.

1. What is the probability that the average amount of paid time lost during a three-month period for the 100 blue-collar workers will exceed 1.5 days?

2. What is the probability that the average amount of unpaid time lost during a three-month period for the 100 blue-collar workers will be between 1.4 and 1.5 days? Please give a precise explanation, as if you are telling someone who doesn’t know anything about statistics, for the reasoning behind your answer?

3. How large a random sample is needed to construct a 95 percent confidence interval for the mean for population paid time lost with a margin of error equal to 0.1? Please give a precise explanation, as if you are telling someone who doesn't know anything about statistics for the reasoning behind your answer.

) 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.

Family Sex Ratio	O	E	(O-E)	(O-E)2	(O-E)2/2
All Boys	235
3B:1G	898
2B:2G	1317
1B:3G	841
All girls	181
Total					X2 =

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:

Sex	O	E	(O-E)	(O-E)2	(O-E)2/E
Male
Female
Total					X2 =

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.

x:	29	0	18	35	32	18	24	−23	−16	−9
y:	18	−4	20	17	22	11	28	−2	−8	−6

(a) Compute Σx, Σx², Σy, Σy².

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.)

	x	y
x
s2
s

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

	x	y
Lower Limit
Upper Limit

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.

Low HS	Medium HS	High HS
4	14	22
9	12	26
6	3	13
8	26	20
14	15	27
16	19	19
8	17	16
10	5	14

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.

	Low HS	Med HS	High HS
Mean
SD

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.

	Low vs. Med.	Low vs. High	Med. vs. High
Mean difference (absolute value)
p value

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?

	MSbetween (the numerator)
	MSwithin  (the denominator)

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

	MSbetween (the numerator)
	MSwithin  (the denominator)

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

	MSbetween (the numerator)
	MSwithin  (the denominator)

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.