Question
In: Statistics and Probability
Suppose you are a researcher in a hospital. You are experimenting with a new tranquilizer. You...
Suppose you are a researcher in a hospital. You are experimenting with a new tranquilizer. You collect data from a random sample of 11 patients. The period of effectiveness of the tranquilizer for each patient (in hours) is as follows:
| 2.9 |
| 3 |
| 3 |
| 2.5 |
| 2.9 |
| 3 |
| 2.4 |
| 2 |
| 2.5 |
| 2.4 |
| 2.5 |
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?
- normal distribution
- t-distribution
c. Why?
d. What must be true in order to construct a confidence interval in
this situation?
- The population standard deviation must be known
- The population mean must be known
- The sample size must be greater than 30
- The population must be approximately normal
e. Construct a 95% 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 "95% confident" in this problem? Use the
definition of confidence level.
- The confidence interval contains 95% of all samples
- 95% of all simple random samples of size 11 from this population will result in confidence intervals that contain the population mean
- There is a 95% chance that the confidence interval contains the population mean
h. Suppose that the company releases a statement that the mean time
for all patients is 2 hours.
Is this possible?
- No
- Yes
Is it likely?
- No
- Yes
i. Use the results above and make an argument in favor or against
the company's statement. Structure your essay as follows:
- Describe the population and parameter for this situation.
- Describe the sample and statistic for this situation.
- Give a brief explanation of what a confidence interval is.
- Explain what type of confidence interval you can make in this situation and why.
- Interpret the confidence interval for this situation.
- Restate the company's claim and whether you agree with it or not.
- Use the confidence interval to estimate the likelihood of the company's claim being true.
- Suggest what the company should do.
Solutions
orchestra answered 2 years agoRelated Solutions
Suppose you are a researcher in a hospital. You are experimenting with a new tranquilizer. You...
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:
2.8
2.9
2.7
2
2.5
2.7
2
2.2
2.7
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? normal
distribution or...
Suppose you are a researcher in a hospital. You are experimenting with a new tranquilizer. You...
Suppose you are a researcher in a hospital. You are
experimenting with a new tranquilizer. You collect data from a
random sample of 8 patients. The period of effectiveness of the
tranquilizer for each patient (in hours) is as follows:
2.3
2.8
2.3
2.6
2
2
3
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....
Suppose you are a researcher in a hospital. You are experimenting with a new tranquilizer. You...
Suppose you are a researcher in a hospital. You are
experimenting with a new tranquilizer. You collect data from a
random sample of 11 patients. The period of effectiveness of the
tranquilizer for each patient (in hours) is as follows:
2.4
2
2
2
2
2.9
2.2
2.5
2.3
2.8
2.3
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?
normal...
Suppose you are a researcher in a hospital. You are experimenting with a new tranquilizer. You...
Suppose you are a researcher in a hospital. You are
experimenting with a new tranquilizer. You collect data from a
random sample of 11 patients. The period of effectiveness of the
tranquilizer for each patient (in hours) is as follows:
3
3
2.4
2.6
2.4
2
2.2
2.7
2.1
2.5
2.3
What is a point estimate for the population mean length of time.
(Round answer to 4 decimal places)
Which distribution should you use for this problem?
normal distribution
t-distribution...
Suppose you are a researcher in a hospital. You are experimenting with a new tranquilizer. You...
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 2.4 2.7
2.4 2.1 2.1 2.2 2.9 2.1
What is a point estimate for the population mean length of time.
(Round answer to 4 decimal places)
Which distribution should you use for this problem? normal
distribution or t-distribution
What...
Suppose you are a researcher in a hospital. You are experimenting with a new tranquilizer. You...
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:
2.5
2.8
2
2.1
2.6
2.5
2.6
2.6
2.9
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?
normal distribution
t-distribution...
Confidence intervals for the mean Suppose you are a researcher in a hospital. You are experimenting...
Confidence intervals for the mean
Suppose you are a researcher in a hospital. You are
experimenting with a new tranquilizer. You collect data from a
random sample of 10 patients. The period of effectiveness of the
tranquilizer for each patient (in hours) is as follows:
3
2.7
2
2.3
2.4
2.6
2.7
2.2
2.3
2.9
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...
At Community Hospital, the burn center is experimenting with a new plasma compress treatment. A random...
At Community Hospital, the burn center is experimenting with a
new plasma compress treatment. A random sample of
n1 = 308 patients with minor burns received the
plasma compress treatment. Of these patients, it was found that 268
had no visible scars after treatment. Another random sample of
n2 = 420 patients with minor burns received no
plasma compress treatment. For this group, it was found that 97 had
no visible scars after treatment. Let p1 be the
population proportion...
At Community Hospital, the burn center is experimenting with a new plasma compress treatment. A random...
At Community Hospital, the burn center is experimenting with a
new plasma compress treatment. A random sample of
n1 = 302 patients with minor burns received the
plasma compress treatment. Of these patients, it was found that 250
had no visible scars after treatment. Another random sample of
n2 = 440patients with minor burns received no
plasma compress treatment. For this group, it was found that 85 had
no visible scars after treatment. Let p1 be the
population proportion of...
At Community Hospital, the burn center is experimenting with a new plasma compress treatment. A random...
At Community Hospital, the burn center is experimenting with a
new plasma compress treatment. A random sample of n1 = 324 patients
with minor burns received the plasma compress treatment. Of these
patients, it was found that 268 had no visible scars after
treatment. Another random sample of n2 = 418 patients with minor
burns received no plasma compress treatment. For this group, it was
found that 93 had no visible scars after treatment. Let p1 be the
population proportion...
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