A researcher measured the body temperatures of 51 randomly selected adults. Summ

Question

A researcher measured the body temperatures of 51 randomly selected adults. Summary information (in degrees Fahrenheit) is given below: Mean Median98.364 98.349 Stand. dev. 0.712 st quartile 97.750 3rd quartile 98.900 a. Fill in the blanks. Based on these statistics, a 95% confidence interval for the true mean o y en perature an es om a lower bound of Fahrenheit to an upper bound of degrees Fahrenheit. (Round both bounds to 2 decimal places after the decimal point. Type lower bound first. DO NOT PUT PARENTHESES IN YOUR ANSWER, BUT SEPARATE THE LOWER AND UPPER BOUNDS WITH A COMMA.) degrees b. Regardless of your answer to part a, suppose a 99% confidence interval (in degrees Fahrenheit was 981 986) Which of the following is the correct interpretation of this confidence interval? ( A. 99% of all adults have mean body temperatures between 981 and 986 degrees Fahrenheit. 0 B. We're 99% confident that the mean body temperature of adults in this sample is between 98.1 and 98.6 degrees Fahrenheit. O c. We're 99% confident that adults in this sample have body temperatures between 981 and 9 8.6 degrees Fahrenheit. D. We're 99% confident that the mean body temperature of all adults is between 98.1 and 98.6 degrees Fahrenheit. 0 E. Adults have m ean body temperatures between 981 and 986 degrees Fahrenheit 99% of the time.

Explanation / Answer

Here, we have sample size = n = 51
Sample mean = 98.364
Sample standard deviation = 0.712

Confidence interval is given as 95%.

First we can calculate the standard error as below:

SE = sd / sqrt( n ) = 0.712/sqrt(51) = 0.09969994

Here alpha = 1 - (confidence level/100) = 1 - 95/100 = 0.05
Critical probability = 1 - alpha/2 = 1 - 0.05/2 = 1 - 0.025 = 0.975
Degrees of freedom = n - 1 = 51 - 1 = 50

Now we can see the t table and calculate the critical value corresponding to 50 degrees of freedom and cumulative probability of 0.975. Critical value is 2.009

Now we can find the margin of error as below:
ME = critical value * standard error = 2.009 * 0.09969994 = 0.2002972

So confidence interval is mean +- Margin of error
(98.364 - 0.2002972) to (98.364 + 0.2002972)
= 98.1637 to 98.5643

b) Option D is correct.
A confidence interval is a range of numbers that(hopefully) captures the true parameter value of interest.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.