# statistics 3.

A student union wants to obtain a 90% confidence interval for the proportion of “full time” students who hold a part-time job for 20 hours or more per week. For this purpose, they want to interview a sample of full-time students. They want a margin of error to be at most 0.1, i.e., the length of the confidence interval should not exceed 0.2. What is the minimum number of full-time students they should interview?
• A researcher wants to determine the difference between the gestational period (period of pregnancy) for two groups of women, namely, those who had normal pregnancies (group A) and those who suffered from a certain complication during pregnancy known as preeclampsia (group B). The following data shows the gestational periods (in weeks) for a sample of 14 women from group A and of 13 women from group B.
Gestational periods for sample from group A: 40, 41, 38, 40, 40, 39, 39, 41, 41, 40, 40, 40, 39, 38
Gestational periods for sample from group B: 38, 30, 32, 42, 30, 38, 35, 32, 38, 39, 29, 29, 32
Find a 95% confidence interval for the difference between the gestational periods of group A and group B, i.e., group A mean minus group B mean. Assume that the variances of the two groups are equal. State any other assumptions you make.
Hint: This relates to confidence interval for 

1. 👍 0
2. 👎 0
3. 👁 125
1. Here are a few ideas to get you started.

First problem:
Use a formula to find sample size.

Here is one for proportions:
n = [(z-value)^2 * p * q]/E^2
... where n = sample size, z-value is 1.645 (90% confidence interval), p = .5 (when no value is stated), q = 1 - p, ^2 means squared, * means to multiply, and E = 0.1 listed in the problem.
Plug values into the formula and calculate n.

Second problem:
You will need to use a two-sample confidence interval formula. You will also need to calculate mean and standard deviation for both groups.

Here is one:
CI95 = (x1 − x2) ± z-value * √(s1^2/n1 + s2^2/n2)
(Note: * means to multiply)

x1 = mean A
x2 = mean B

z-value = 1.96

s1^2 = standard deviation A (squared)
s2^2 = standard deviation B (squared)

n1 = sample size A
n2 = sample size B

Plug the values into the formula and calculate the interval.

I'll let you take it from here.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Economics (45)

The 2003 Statistical Abstract of the United States reported the percentage of people 18 years of age and older who smoke. Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of

2. ### statistics

Lorraine was in a hurry when she computed a confidence interval for μ. Because σ was not known, she used a Student's t distribution. However, she accidentally used degrees of freedom n instead of n - 1. Will her confidence

3. ### Statistics

Explaining confidence. A student reads that a 95% confidence interval for the mean ideal weight given by adult American women is 140 ± 1.4 pounds. Asked to explain the meaning of this interval, the student says, “95% of all

4. ### Statistics

One of the questions on a survey of 1,000 adults asked if today's children will be better off than their parents (Rasmussen Reports website, October 26, 2012). Representative data are shown in the DATAfile named ChildOutlook. A

1. ### Statistics

To plan the budget for next year a college needs to estimate what impact current economic downturn might have on student requests for financial aid. Historically, this college has provided aid to 35% of its students. Officials

2. ### Statistics

A confidence interval was used to estimate the proportion of statistics students that are females. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Based on the interval

3. ### stat

One of the questions on a survey of 1,000 adults asked if today's children will be better off than their parents (Rasmussen Reports website, October 26, 2012). Representative data are shown in the WEBfile named ChildOutlook. A

4. ### Stastics

Which of the following descriptions of confidence intervals is correct? (Select all that apply) a. If a 95% confidence interval contains 0, then the 99% confidence interval contains 0 b. If a 99% confidence interval contains 0,

1. ### Elementary Statistics

1) Construct a confidence interval of the population proportion at the given level of confidence. x=60,n=300, 99% confidence. The 99% confidence interval is (_,_) 2) A researcher wishes to estimate the proportion of adults who

2. ### Stats

One of the questions on a survey of 1,000 adults asked if today's children will be better off than their parents (Rasmussen Reports website October 26, 2012). Representative data are shown in the file ChildOutlook. A response of

3. ### Statistics

5. A random sample of size 81 has sample mean 20 and sample standard deviation 3. (a) Is it appropriate to use a Student’s t distribution to compute a confidence interval for the population mean μ? Explain. (1 mark) (b) Find a

4. ### Statistics

A confidence interval for a population mean has a margin of error of 3.1. a)Determine the length of the confidence interval. b)If the sample mean is 56.7, obtain the confidence interval.
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}