Question

1. Carl Reinhold August Wunderlich reported that the
mean temperature of humans is 98.6F. To test this long-held belief
about the average body temperature, medical researchers measured
the temperature of 36 randomly selected healthy adults. The sample
data resulted in a sample mean of 98.2F and a sample standard
deviation of 0.6F. Assuming that the population is normal, test
whether the mean temperature of humans is different from 98.6F at
the 5% significance level. To gain full credit, you should provide
the following

(a) State and check the modeling assumptions.

(b) Define the parameter of interest.

(c) State the hypotheses.

(d) Calculate the value of the test statistic. What is
the distribution of the test statistic?

(e) Find the p-value using the appropriate table.

(f) State the decision and the conclusion in the
context of the problem.

(g) Calculate a 95% confidence interval for the
population mean µ and interpret your interval in the context of
this problem.

(h) Could we have used the 95% confidence interval
calculated in

(g) to make a decision about the hypothesis test conducted?
Discuss, in depth, why or why not this can be done.

Answer #1

here we want to test,: μ = 98.6 vs : ≠ 98.6

the population standard deviation is unknown. so, we perform the one sample t test.

the test statistic T = which follows t distribution with df n-1 under the null hypothesis.

here the value of t statistic is T= -4.00

we reject at level 0.05, if

= 2.0315

thus,

hence we reject the null hypothesis at 5 % level of significance

thus, 95% CI is given by (97.997, 98.403)

It has long been stated that the mean temperature of humans
is
98.698.6degrees°F.
However, two researchers currently involved in the subject
thought that the mean temperature of humans is less than
98.698.6degrees°F.
They measured the temperatures of
4444
healthy adults 1 to 4 times daily for 3 days, obtaining
200200
measurements. The sample data resulted in a sample mean of
98.398.3degrees°F
and a sample standard deviation of
0.90.9degrees°F.
Use the P-value approach to conduct a hypothesis test to judge
whether...

A data set includes 109 body temperatures of healthy adult
humans having a mean of 98.3°F and a standard deviation of
0.54°F.
Construct a 99% confidence interval estimate of the mean body
temperature of all healthy humans.
_______________ _________________
Round to three decimal places as needed.
Use your responses from question 1, to answer question 2.
What does the sample suggest about the use of 98.6°F
as the mean body temperature?
Group of answer choices
A. This suggests that the mean...

It has long been stated that the mean temperature of humans is
98.6 degrees F. However, two researchers currently involved in the
subject thought that the mean temperature of humans is less than
98.6 degrees F. They measured the temperatures of 61 healthy adults
1 to 4 times daily for 3 days, obtaining 275 measurements. The
sample data resulted in a sample mean of 98.2 degrees F and a
sample standard deviation of 1.1 degrees F. Use the P-value
approach...

2. The College Board reported that the mean SAT score in 2009
was 540 for all US High School students that took the SAT. A
teacher believes that the mean score for his students is greater
than 540. He takes a random sample of 50 of his students and the
sample mean score for the 25 students is 565 with a sample standard
deviation of 100. Does he have evidence that his students, on
average, do better than the national...

Question 4:
An article in Wikipedia claims that the mean body
temperature of adults is less than 98.6° F. This goes against
everything you’ve ever been taught, so you gather 565 healthy
adults and observe a mean body temperature of 98.2°F, with the
sample standard deviation of 2.6°F. Test the article’s claim at a
5% level of significance.
If the problem is a confidence interval:
Show whether the criteria for approximate normality are
met. (1 point)
Summarize the sample statistics....

1)A data set includes 108 body temperatures of healthy adult
humans having a mean of 98.2degreesF and a standard deviation of
0.64degreesF. Construct a 99% confidence interval estimate of the
mean body temperature of all healthy humans. What does the sample
suggest about the use of 98.6degreesF as the mean body
temperature? What is the confidence interval estimate of the
population mean mu?
2)A clinical trial was conducted to test the effectiveness of a
drug for treating insomnia in older...

It has long been stated that the mean temperature of humans is
98.6degrees°F. However, two researchers currently involved in the
subject thought that the mean temperature of humans is less than
98.6degrees°F. They measured the temperatures of 61 healthy adults
1 to 4 times daily for 3 days, obtaining 275 measurements. The
sample data resulted in a sample mean of 98.2degrees°F and a sample
standard deviation of 1.1degrees°F. Use the P-value approach to
conduct a hypothesis test to judge whether...

It has long been stated that the mean temperature of humans is
98.6degreesF. However, two researchers currently involved in the
subject thought that the mean temperature of humans is less than
98.6degreesF. They measured the temperatures of 44 healthy adults 1
to 4 times daily for 3 days, obtaining 200 measurements. The
sample data resulted in a sample mean of 98.3degreesF and a sample
standard deviation of 1degreesF. Use the P-value approach to
conduct a hypothesis test to judge whether...

The distribution of blood cholesterol level in the population of
all male patients 20–34 years of age tested in a large hospital
over a 10-year period is close to Normal with standard deviation σ
= 48 mg/dL (milligrams per deciliter). At your clinic, you measure
the blood cholesterol of 14 male patients in that age range. The
mean level for these 14 patients is x̄ = 180 mg/dL. Assume that σ
is the same as in the general male hospital...

1. TRUE or FALSE State whether the statement is true or false,
and also give a brief sentence explaining why you believe this.
(a) If we decrease the confidence level for a fixed n, we
decrease the width of the confidence interval.
(b) A research article reports that a 95% confidence interval
for mean reaction time is from 0.25 to 0.29 seconds. About 95% of
individuals will have reaction times in this interval.
c) In a hypothesis test, a p-value...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 9 minutes ago

asked 15 minutes ago

asked 16 minutes ago

asked 27 minutes ago

asked 50 minutes ago

asked 54 minutes ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago