1. Assuming that the distribution is

normal for weight relative to the ideal and 99% of the male participants scored

between (53.68, 64.64), where did 95% of the values for weight relative to the

ideal lie? Round your answer to two decimal places.

A. -17.5,

28.4

B. -39.5,

50.4

C. -40.4,

51.3

D. -53.7,

64.6

Answer:

Choose an item.

Please provide a few steps

for answering this question:

2. Which of the following values from Table 1 tells us

about variability of the scores in a distribution?

A. 11.94

B. 20.46

C. 22.57

D. 53.66

E. 60.22

Answer:

Choose an item.

Please provide a few steps

for answering this question:

3. Assuming

that the distribution for General Health Perceptions is normal, 95% of the

females scores around the mean were between what values? Round your answer to

two decimal places.

A. 14.25, 65.17

B. -8.66, 88.08

C. -10.19,89.61

D. -25.98,105.40

Answer:

Choose an item.

Please provide a few steps

for answering this question:

4. Assuming that the distribution of scores for Pain

is normal, 95% of the mens scores around the mean were between what two

values? Round your answer to two decimal places.

A. 21.63 83.43

B. -6.18 111.24

C. -8.03 113.09

D. -27.06 132.12

Answer:

Choose an item.

Please provide a few steps

for answering this question:

5. Were the body image scores significantly different

for women versus men? Provide a rationale for your answer.

Is the following statement is correct?

Body image scores on the 0-100 scale were meaningfully

(F (1, 37) =5.41, p=0.03) higher for women than for men.

A. Yes.

B. No

Answer:

Choose an item.

Please provide a few steps

for answering this question:

6. Assuming that the distribution of Mental Health

scores for men is normal, where are 99% of the mens mental health scores

around the mean in this distribution? Round your answer to two decimal places.

A. 33.33, 80.85

B. 11.95, 102.23

C. 10.52, 103.66

D. -4.11, 118.29

E. -61.71,175.89

Answer:

Choose an item.

Please provide a few steps

for answering this question:

7. Assuming that the

distribution of scores for Physical Functioning in women is normal, where are

99% of the women’s scores around the mean in this distribution? Round your

answer to two decimal places.

A. 35.41, 94.99

B. 8.60, 121.80

C. 6.81, 123.59

D. -11.53, 141.93

E. -83.75, 214.15

Answer:

Choose an item.

Please provide a few steps

for answering this question:

8. Assuming that the

distribution of scores is normal, 99% of HIV-positive body image scores around

the mean were between what two values? Round your answer to two decimal places.

A. 51.00, 85.00

B. 35.70, 100.30

C. 34.68, 101.32

D. 24.21, 111.79

E. -17.00,153.00

Answer:

Choose an item.

Please provide a few steps

for answering this question:

9.

Assuming that the distribution of scores for Role Functioning is normal, 99% of

the men’s scores around the mean were between what values? Round your answer to

two decimal places.

A. 3.71, 96.29

B. -37.95,137.95

C. -40.73,140.73

D. -69.24,169.24

E. -181.45,

281.45

Answer:

Choose an item.

Please provide a few steps

for answering this question:

10. What are some of the

limitations of this study that decrease the potential for generalizing the

findings to the target population?

A. The

sample was chosen from the primary care setting (it is likely not representative

of the entire target population).

B. Small

sample size.

C. All

above.

Answer:

Choose an item.

Please provide a rationale

for answering this question:

Grading

Please do not make any changes for the following

grading table unless you have a problem with the drop-down lists (then you can

enter your answers in the second column).

If you use the drop-down lists, the instructor will update your answers

in the table. Thanks

Question

Your

answer

Correct

answer

Possible points

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Where did 95% of the values for weight relative to the ideal lie assuming a normal distribution and given a specific range of scores for male participants?

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Introduction: In statistical analysis, normal distribution is a common approach to understand a vast range of data derived from different areas. This process helps to determine the proportion of value distribution around the mean, standard deviation, and variance. The current article analyzes normal distribution data to answer various questions related to weight, health perceptions, pain, and other areas of men and women’s health.

Description: The article discusses nine different questions based on normal distributions. The first question aims to determine where 95% of the values for weight relative to the ideal range for men lie. The second question is related to identifying which value from Table 1 shows the variability of scores. The next two questions analyze the normal distribution of scores for General Health Perceptions of females and Pain for males to understand the range of scores for 95% of the participants. The fifth question analyzes if the body image scores were significantly different for women versus men and provides a rationale for the answer. The next two questions are related to determining the range of mental health scores for men and physical functioning scores for women to find the scores’ distribution around the mean for 99% of the participants. Finally, the article concludes by discussing the range of scores for Role Functioning in men for 99% of the participants.

Objectives:

1. To understand the concept of normal distribution in statistics.

2. To be able to calculate the proportion of data within a given range in a normal distribution.

3. To identify the measure of variability of scores in a distribution.

4. To determine the range of scores within a given proportion of data in a normal distribution.

5. To interpret the results of a statistical test and draw conclusions.

Learning Outcomes:

1. Understand the characteristics of a normal distribution such as mean, median, and mode.

2. Calculate the proportion of data within a given range using the z-score formula.

3. Identify the standard deviation as a measure of variability in a distribution.

4. Calculate the range of scores within a given proportion of data using the z-score formula.

5. Interpret the results of a statistical test and draw conclusions based on the p-value and statistical significance.

Solution 1:

Assuming that the distribution is normal for weight relative to the ideal and 99% of the male participants scored between (53.68, 64.64), we can use the z-table to find where 95% of the values lie.

We know that the mean is halfway between the upper and lower limits (mean = 59.16). Using the formula for the z-score, we can find the number of standard deviations from the mean:

z = (x – mean) / standard deviation

We want to find the x-values that correspond to a z-score of +/-1.96, which covers 95% of the distribution.

-1.96 = (x – 59.16) / s

1.96 = (x – 59.16) / s

Solving for x:

x = -1.96s + 59.16

x = 1.96s + 59.16

We know that the range of scores is 10.96 (64.64 – 53.68). To find the standard deviation, we can use the formula:

s = range / (2 * 1.96)

s = 10.96 / (2 * 1.96)

s = 1.4

Substituting s into the formulas we found above:

x = -1.96(1.4) + 59.16

x = 55.40

x = 1.96(1.4) + 59.16

x = 62.92

Therefore, 95% of the values for weight relative to the ideal lie between 55.40 and 62.92.

Solution 2:

To answer whether body image scores were significantly different for women versus men and whether the statement “Body image scores on the 0-100 scale were meaningfully (F (1, 37) =5.41, p=0.03) higher for women than for men” is correct, we need to interpret the F-value and p-value.

The F-value is a measure of variation between groups relative to variation within groups, and a higher F-value suggests that the groups are different. The p-value represents the probability that the results are due to chance. A p-value less than 0.05 is generally considered statistically significant.

In this case, the F-value is 5.41 with 1 degree of freedom for the numerator (between groups) and 37 degrees of freedom for the denominator (within groups). The p-value is 0.03.

Since the p-value is less than 0.05, we can conclude that the difference between body image scores for women and men is statistically significant. The statement is therefore correct.

Suggested Resources/Books:

1. “Statistics for Health Care Research: A Practical Workbook” by Susan K. Grove and Daisha J. Cipher

2. “Basic Statistics for the Health Sciences” by Jan W. Kuzma and Frank J. Irwin

3. “Biostatistics for the Biological and Health Sciences” by Marc M. Triola, Mario F. Triola, and Jason Roy

Similar asked questions:

1. What is the formula for calculating the mean of a normal distribution?

2. How do you interpret a 95% confidence interval in a normal distribution?

3. What is the difference between a parameter and a statistic in inferential statistics?

4. How do you determine if a distribution is normal?

5. What is the purpose of hypothesis testing in statistics?

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