Allen Shoemaker, from Calvin College, produced a data set with the same properties as the original temperature readings. His data set consists of one oral temperature reading for each of the 130 randomly chosen, healthy 18- to 40-year-olds. A dotplot of Shoemaker's temperature data is shown below. A vertical line at 98.6oF was added for reference. Exploratory data analysis revealed several interesting facts about this data set: The mean temperature was x ¯ = 98.25 o F The standard deviation of the temperature reading was s x = 0.73 o F 62.3% of the temperature readings were less than 98.6oF. If "normal" body temperature really is 98.6oF, we would expect that about half of all healthy 18- to 40-year-olds will have a body temperature less than 98.6oF. Do the data from this study provide convincing evidence at the α = 0.05 significance level that this is not the case? Using the p-value (or critical values & test statistic), draw a proper conclusion and write said conclusion in context. Based on your conclusion, which type of error could have been made: a Type I error or a Type II error. Justify your answer. If you were a researcher, what type of data would you be interested in collecting? What would your null and alternative hypotheses be?
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
I was told to submit the questions again with the other answers so i can get the other 3 answer. Thanks
Do You Have a Fever?
Sometimes when you are sick, your forehead feels really warm. You might have fever. How can you find out whether you do? By taking your temperature , of course. But what temperature should the thermometer show if your're healthy? Is this temperature the same for everyone?
Several years ago, researchers conducted a study to determine whether the "accepted" value for normal body temperature, 98.6oF, is accurate. They used an oral thermometer to measure the temperatures of a random sample of healthy men and women aged 18 to 40. As is often the case, the researchers did not provide their original data.
Allen Shoemaker, from Calvin College, produced a data set with the same properties as the original temperature readings. His data set consists of one oral temperature reading for each of the 130 randomly chosen, healthy 18- to 40-year-olds. A dotplot of Shoemaker's temperature data is shown below. A vertical line at 98.6oF was added for reference.
Exploratory data analysis revealed several interesting facts about this data set:
- The mean temperature was x ¯ = 98.25 o F
- The standard deviation of the temperature reading was s x = 0.73 o F
- 62.3% of the temperature readings were less than 98.6oF.
If "normal" body temperature really is 98.6oF, we would expect that about half of all healthy 18- to 40-year-olds will have a body temperature less than 98.6oF. Do the data from this study provide convincing evidence at the α = 0.05 significance level that this is not the case?
-
- Using the p-value (or critical values & test statistic), draw a proper conclusion and write said conclusion in context.
- Based on your conclusion, which type of error could have been made: a Type I error or a Type II error. Justify your answer.
- If you were a researcher, what type of data would you be interested in collecting? What would your null and alternative hypotheses be?
Expert Answer
(1). Type of test:
The investigator is specifically interested to test whether half of all healthy 18– to 40–year-olds will have a body temperature less than 98.60 F or not.
Evidently, the test is to determine whether the population proportion of temperature readings that are less than 98.60 F is 0.5 or not.
Thus, the study seeks to find whether the population proportion of temperature readings that are less than 98.60 F is 0.5 or not.
In other words, the study aims to test the equality of a single proportion.
Therefore, the appropriate test to be performed is one proportion Z test.
(2). Conditions required to perform one sample proportion test:
The required conditions to perform one sample proportion test are given below:
- The sample must be randomly selected from the population.
- The size of the population should be at least 10 times larger than the population. That is, N ≥ 10n.
- The
expected values of success and failure must be at least 10. That is, np ≥ 10 and n(1-p) ≥ 10.
Check for the conditions:
Given that a simple random sample of 130 healthy 18– to 40–year-olds are selected.
This infers that the sample is selected randomly from the population.
The sample size is n = 130, the total number of healthy 18– to 40–year-olds I will be very large. That is, the population size will be very large. Hence, the population will be at least 10 times larger than the sample.
The expected values of success and failure are obtained as given below:
Therefore, all conditions are met to perform a one sample proportion test.
Test statistic:
The sample size is n = 130.
It is given that, 62.3% of the temperature readings were less than 98.60 F.
The sample proportion is p^ = 0.986.
The population proportion is p = 0.5.
The test statistic is obtained as 11.0825 from the calculations given below:
Thus, the test statistic value is 11.0825.
P-value:
The test statistic is z = 11.0825.
The hypothesis test is two tailed.
The P-value is obtained as 0 from the calculation given below:
Thus, the P-value is 0.
Decision rule:
The level of significance is α = 0.05.
Decision rule based on P-value approach:
If P-value ≤ α, then reject the null hypothesis H0.
If P-value > α, then fail to reject the null hypothesis H0.
Conclusion based on P-value approach:
The P-value is 0 and α value is 0.05.
Here, P-value is less than the value.
That is, 0 (=P-value) < 0.05 (=α).
By the rejection rule, reject the null hypothesis H0.
Therefore, reject the null hypothesis.
Hence, there is not enough evidence to conclude that population proportion of temperature readings that are less than 98.60 F is 0.5.
Therefore, there is not sufficient evidence to support the claim that half of all healthy 18– to 40–year-olds will have a body temperature less than 98.60 F.
Yes, the data from this study provide convincing evidence at the α = 0.05 significance level that this is not the case.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images
1. Does the data provide convincing evidence that the true
2. A 95% confidence interval for the population mean is 98.123 F to 98.377 F. Explain how the confidence interval is consistent with, but gives more information than, the significance test in the previous question.
by Bartleby Expert
