SOLUTION: 1 Test the claim that the mean body temperature of normal and healthy adults is equal to 37°C. Sample data consist of 20 randomly selected healthy adults who have body temper

Question 1207829: 1 Test the claim that the mean body temperature of normal and healthy adults is equal
to 37°C. Sample data consist of 20 randomly selected healthy adults who have
body temperatures with a mean of 36.78° and a standard deviation of 0.35°. Use a
0.05 level of significance.
2. Using the same sample data given in problem 1, test the claim that the standard
deviation of body temperatures for normal healthy adults is less than 1.00°C. Use a
0.05 level of significance.
3. Use a 0.05 level of significance to test Bill Bradley’s claim that the majority of voters
would vote for him. Assume that sample data consist of 1068 randomly selected
voters, 540 of whom indicated that they would vote for Bradley.
4. The Sylvan Pharmaceutical Company makes tubes of antibacterial cream that are
labeled as containing 4 oz. In testing the claim that the mean content amount is less
than 4 oz., a P-value of 0.220 is obtained. What do you conclude?
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Please ask only one question per post.
I'll do problem 1 to get you started.

n = 20 = sample size
mu = 37 = the claimed population mean body temperature
xbar = 36.78 = sample mean body temperature
s = 0.35 = sample standard deviation of the temperatures
sigma = population standard deviation = unknown
alpha = level of significance = 0.05

Null Hypothesis: mu = 37
Alternative Hypothesis: mu =/= 37
The claim is made in the null.
The alternative hypothesis indicates we have a two-tailed test.

We don't know the value of sigma and n > 30 is not the case, so we must use the T distribution.
df = degrees of freedom
df = n-1
df = 20-1
df = 19

Use a T table such as this one
https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf
Such a table can be found at the back of your stats textbook.
Highlight the df = 19 row and the column that mentions "two tails = 0.05" since this is the alpha level.
The intersection of this row and column yields the approximate t critical value t = 2.093

What does this tell us?
It tells us that P(-2.093 < t < 2.093) = 0.95 approximately when df = 19.
The 0.95 is the area of the main body while 1-0.95 = 0.05 is the combined area of the two tails.

If the test statistic is in the interval -2.093 < t < 2.093, then we do not reject the null.
Otherwise, we'll reject the null.

Let's compute the test statistic.
testStatistic = (xbar - mu)/( s/sqrt(n) )
testStatistic = (36.78 - 37)/( 0.35/sqrt(20) )
testStatistic = -2.811 approximately

The value t = -2.811 is NOT in the interval -2.093 < t < 2.093
This value is in the rejection region. It's to the left of the interval mentioned.
Therefore we'll reject the null and conclude that mu =/= 37 must be the case.
The claim "the mean body temperature of normal and healthy adults is equal to 37°C" appears to be false.
Either mu > 37 or mu < 37.

--------------------------------------------------------------------------

Another approach using p-value

We calculated the test statistic to be roughly -2.811
Let's find the value of P(t < -2.811)
Use a stats calculator such as a TI83 to determine that P(t < -2.811) = 0.00558 approximately when df = 19.

We're doing a two-tailed test, so don't forget to double that result and you would get 2*0.00558 = 0.01116
This is the approximate p-value.
It is smaller than alpha (0.05), so we must reject the null.

A useful phrase to remember: "If the p-value is low, then the null must go" which would translate to "if the p-value is smaller than alpha, reject the null".

RELATED QUESTIONS
We have a sample of 106 body temperatures having a mean of 98.2°F. Assume that the... (answered by ewatrrr)

In a 1868 paper, German physician Carl Wunderlich reported based on over a million body... (answered by Boreal)

2. Assume the body temperatures of healthy adults are normally distributed with a mean... (answered by stanbon)

2. Assume the body temperatures of healthy adults are normally distributed with a mean of (answered by stanbon)

2. Assume the body temperatures of healthy adults are normally distributed with a mean of (answered by Fombitz)

2. Assume the body temperatures of healthy adults are normally distributed with a mean of (answered by ladun6)

2. Assume the body temperatures of healthy adults are normally distributed with a mean of (answered by stanbon)

A fever is any body temperature above the mean temperature, in practice a person is... (answered by Boreal)

An 1868 paper by German physician Carl Wunderlich reported, based on over a million body... (answered by Boreal)