The amount of calcium in the blood was compared for men and women of the same age. Researchers measured the serum calcium (mmol/l) for 91 men and 84 women. The data are summarised below. Mean Std. Dev. Men 2.318 0.122 Women 2.397 0.137 a) Do men and women of this age have significantly different serum calcium levels? Carry out a hypothesis test with a significance level of 5%. b) Create a 95% confidence interval for the mean difference in serum calcium, and interpret the interval. c) Is the confidence interval consistent with your conclusion from a)? Explain. d) Is it necessary for the test you used that serum calcium is normally distributed? Explain.
Added by Nate C.
Step 1
The null hypothesis is that there is no difference between the mean serum calcium levels of men and women, while the alternative hypothesis is that there is a difference. Using a significance level of 5%, we have: H0: μmen - μwomen = 0 Ha: μmen - μwomen ≠ Show more…
Show all steps
Close
Your feedback will help us improve your experience
Amman Zia and 88 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The level of calcium in the blood of healthy young adults follows a Normal distribution, with mean 9.5 milligrams per deciliter and standard deviation 0.5. A medical professional is concerned that the calcium level in a population of pregnant young women who attend a clinic is too low. The clinic measures blood calcium levels of 25 pregnant young women at their first visit for prenatal care. The mean of these 25 measurements is 9.1. a. (5 marks) Draw a rough sketch of the distribution of sample mean calcium level. [Make sure to indicate important points and label the axis.] b. (8 marks) Do the data provide evidence to support the medical professional's concern? i. What are the hypotheses you would test? {Make sure to use statistical notation]. ii. What is the test statistic you would use? What is its distribution? iii. Calculate the test statistic. iv. State your conclusion using a 5% level of significance. v. Explain your conclusion in the context of the problem.
Sheryl E.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD