# Confidence Intervals

*label*Mathematics

*timer*Asked: Dec 20th, 2017

*account_balance_wallet*$15

**Question description**

For this Discussion, you will explore the relationship between these components and understand the trade-off between reducing risk in our confidence of estimates and increasing precision.

**To prepare for this Discussion:**

- Review Chapters 6 and 7 of the Frankfort-Nachmias & Leon-Guerrero text and in Chapter 8, p. 256, consider the 2012 Benghazi Terrorist Attack Investigation and focus on how different levels of confidence and sample size work together.
- Review Magnusson’s web blog found in the Learning Resources to further your visualization and understanding of confidence intervals.
- Use the Course Guide and Assignment Help found in this week’s Learning Resources to search for a quantitative article related to confidence intervals.
- Using the SPSS software, General Social Survey dataset and choose a quantitative variable that interests you.

#### By Day 3

Using SPSS:

- Take a random sample of 100.
- Calculate the 95% confidence interval for the variable.
- Calculate a 90% confidence interval.
- Take another random sample of 400.
- Calculate the 95% confidence interval for the variable.
- Calculate a 90% confidence interval.

Post your results and an explanation of how different levels of confidence and sample size affect the width of the confidence interval. Next, consider the statement, “Confidence intervals are underutilized” and explain what the implications might be of using or not using confidence intervals. Provide examples based on the results of your data. Also, use your research to support your findings.

Be sure to support your Main Post and Response Post with reference to the week’s Learning Resources and other scholarly evidence in APA Style.Frankfort-Nachmias, C., & Leon-Guerrero, A. (2018).

Social statistics for a diverse society(8th ed.). Thousand Oaks, CA: Sage Publications.

- Chapter 5, “The Normal Distribution” (pp. 128-150)
- Chapter 6, “Sampling and Sampling Distributions” (pp. 151-178)
- Chapter 7, “Estimation” (pp. 179-201)

## Tutor Answer

See attached

Confidence Intervals.

To determine how the width of confidence intervals is affected by confidence level and

sample size, two variables random1 and random2 were generated randomly using SPPS random

number generation. The generated numbers were between 200 and 700. For the variable

random1 a total of 100 random numbers were generated while for the variable random2 a total of

400 random numbers were created.

Based on the two variables, the following confidence intervals were obtained

Random1 (N=100)

One-Sample Statistics

N

Mean

Std.

Deviation

Std. Error

Mean

random1

100 457.90

155.840

15.584

Table1: Descriptive statistics random1

One-Sample Test

Test Value = 0

t

random1

Sig. (2tailed)

df

29.383

99

Mean

Difference

.000

457.902

95% Confidence Interval of

the Difference

Lower

426.98

Upper

488.82

Table 2: 95% confidence interval for random1

One-Sample Test

Test Value = 0

t

random1

29.383

Sig. (2tailed)

df

99

.000

Table 3: 90% confidence interval for random1

Random2 (N=400)

Mean

Difference

457.902

90% Confidence Interval of

the Difference

Lower

432.03

Upper

483.78

One-Sample Statistics

N

Std.

Deviation

Mean

Std. Error

Mean

random2

400 463.83

138.258

Table 4: Descriptive statistics random2

6.913

One-Sample Test

Test Value = 0

t

random2

Sig. (2tailed)

df

67.097

399

Mean...

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