Researchers compared cortisol levels of two samples of women at childbirth. The first group (n=48) underwent emergency cesarean section following induced labor and had a mean cortisol level of 445 with a standard deviation of 60. The second group (n=50) delivered either by cesarean section or vaginally following spontaneous labor, and had a mean cortisol level of 650 with a standard deviation of 75. Construct a two-sided 95% confidence interval for the difference between the two means. Assume equal variances. Give an interpretation of the confidence interval. You MUST show your work to receive full credit. Partial credit is available.

Question
Asked Oct 29, 2019
1 views

Researchers compared cortisol levels of two samples of women at childbirth. The first group (n=48) underwent emergency cesarean section following induced labor and had a mean cortisol level of 445 with a standard deviation of 60. The second group (n=50) delivered either by cesarean section or vaginally following spontaneous labor, and had a mean cortisol level of 650 with a standard deviation of 75. Construct a two-sided 95% confidence interval for the difference between the two means. Assume equal variances. Give an interpretation of the confidence interval. You MUST show your work to receive full credit. Partial credit is available.

check_circle

Expert Answer

Step 1

 

Solution:

The critical value is obtained below:

From the given information, the first group sample size n1 is 48, standard deviation s1 is 60 and mean is 445. The second group sample size n2 is 50, standard deviation s1 is 75 and mean is 650. The confidence level is 95%.

The level of significance=1-0.95=0.05.

The degrees of freedom= n1+n2–2=48+50-2=96

The critical value is,

From the EXCEL, using the formula, =T.INV.2T(0.05,5), the critical value is 1.985.

Step 2

The two-sided 95% confidence interval for the difference between the two means is constructed below:

The required 95%confidence interval is,

help_outline

Image Transcriptionclose

S& 1 п п, CI=(x-)tt (n-1)s +(n-1)s,1 1 nn-2 п, (48-1)(60) +(50-1)(75) 48+50 2 1 (445 650)t1.985, 48 50 -(-232.3,-177.7)

fullscreen
Step 3

The confidence interval is interpreted below:

There is 95% confident that difference between the two means lies between &nda...

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Statistics

Other

Related Statistics Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: The following data represent the number of games played in each series of an annual tournament from ...

A: From the given information:X(game played)4567Frequency18162020 a.Construct a discrete probability di...

question_answer

Q: Assume that x has a normal distribution with the specified mean and standard deviation. Find the ind...

A: Given:Mean=28Standard deviation=3.4 

question_answer

Q: Which is better and corresponds to the higher relative position, a score of 92 on a test with a mean...

A: Solution:From the given information, score of 92 on a test with standard deviation of 15 and mean of...

question_answer

Q: A sample is selected from a population with μ = 52, and a treatment is administered to the sample. I...

A:  The greatest likelihood of reject the null hypothesis is occurred when z-score (calculated value) i...

question_answer

Q: 27. Call me: A sociologist wants to construct a 95% confidence interval for the proportion of childr...

A: It is given that margin of error (E) is 0.02 and the confidence level is 95%.Here,

question_answer

Q: For the most recent years available, the mean annual cost to attend a private university in the Unit...

A: Consider, X be the random variable that represents annual cost to attend a private university. It is...

question_answer

Q: Use a table of t-values to estimate the P-value for the specified one-mean t-test.  Tight-tailed tes...

A: Solution:The degrees of freedom is obtained below:From the given information, sample size is 19, tes...

question_answer

Q: Consider a bimominal experiment with 2 trials and p=0.4 d. Find the probability of at least one succ...

A: It is given that n = 2 and p = 0.4. Therefore, q = 1–p = 0.6.The PMF of binomial distribution is giv...

question_answer

Q: #3: Let Z bee normally distributed with mean 0 and variance 1. Let Z1,..., Zn be an i.i.d. random sa...

A: Solution:3.a. The moment generating function of Z2 is obtained below:From the given information, z b...