Answered: Suppose you are a researcher in a…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 13PPS

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Question

Suppose you are a researcher in a hospital. You are experimenting with a new tranquilizer. You collect data from a random sample of 9 patients. The period of effectiveness of the tranquilizer for each patient (in hours) is as follows:

2.3
3
2.1
2.7
2.3
2.7
2.2
2.4
2.2

a. What is a point estimate for the population mean length of time. (Round answer to 4 decimal places)

b. Which distribution should you use for this problem?

t-distribution
normal distribution

c. Why?

d. What must be true in order to construct a confidence interval in this situation?

The sample size must be greater than 30
The population mean must be known
The population standard deviation must be known
The population must be approximately normal

e. Construct a 99% confidence interval for the population mean length of time. Enter your answer as an open-interval (i.e., parentheses) Round upper and lower bounds to two decimal places

f. Interpret the confidence interval in a complete sentence. Make sure you include units

g. What does it mean to be "99% confident" in this problem? Use the definition of confidence level.

99% of all simple random samples of size 9 from this population will result in confidence intervals that contain the population mean
There is a 99% chance that the confidence interval contains the population mean
The confidence interval contains 99% of all samples

h. Suppose that the company releases a statement that the mean time for all patients is 2 hours.

Is this possible?

Is it likely?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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