Use attached data consisting of a simple random sample of body temperatures (in Fahrenheit) of 23 healthy adults. Use a graphing calculator to answer the following questions:
1. What is the mean body temperature?
2. What is the standard deviation of body temperatures?
3. Construct a 90% confidence interval estimate of the mean body temperature of all adults by following these steps:
a) Verify requirements (provide a graph if needed)
b) Find the critical value (either or , whichever is appropriate)
c) Find the Margin of Error E.
d) State the confidence interval.
e) Explain what this Confidence Interval means.
f) It is believed that the mean body temperature of all healthy adults is 98.60F. Does your confidence interval suggest that this might be the true mean? Explain!
4. Using the same information, construct a confidence interval for each given confidence level (you don’t have to show your work. Just complete the table below).
Confidence level Margin of Error Confidence Interval
80%
95%
99%
5. What happens to the Margin of Error as the confidence level increases? Does the width of the confidence interval increase or decrease? Explain why this happens.
6. How many adults should be sampled to obtain a 95% confidence interval of the mean body temperature of all adults? Assume that we want to be within 0.20F from the true mean. Use standard deviation obtained in question 2.
Part II (10 pts)
1. In two or three complete sentences, explain what a Confidence Interval means (in general), as if you were talking to someone who has not taken statistics.
2. Can we be 100% confident that our confidence interval contains the population parameter we are trying to estimate? Explain.
Part III (10 pts)
Explain hypothesis testing to a friend, using the following scenario as a model. Describe the hypotheses, the sample statistic, the P-value, the meanings of type I and type II errors, and the level of significance. Discuss the significance of the results. Formulas are not required.
A team of research doctors designed a new knee surgery technique utilizing much smaller incisions than the standard method. They believe recovery times are shorter when the new method is used. Under the old method, the average recovery time for full use of the knee is 4.5 months. A random sample of 38 surgeries using the new method showed the average recovery time to be 3.6 months, with sample standard deviation of 1.7 months. The P-value for the test is 0.0011. The research team states that the results are statistically significant at the 1% level of significance.
Part IV (40 pts)
Refer to the attached dataset ‘Weights of Coke.txt .
1. Test the claim that because they contain the same amount of cola, the mean weight of cola in cans of regular coke is the same as the mean weight of cola in cans of Diet Coke.
a) Which test applies for this problem? Explain why. Use the order calculator below and get started! Contact our live support team for any assistance or inquiry.
b) Verify the requirements
c) State the claim, the null and alternative Hypotheses (H0 and H1).
d) Find descriptive statistics required for this test.
e) Find the test statistic using Statdisk (Analysis/ Hypothesis Testing).
f) What is the number of degrees of freedom?
g) Find the P-value
h) In your own words explain the meaning of the p-value for this particular problem (don’t just write if p