Question

8. For a healthy adult female, red blood cell count has a mean of 4.8 million cells per cubic millimeter of whole blood. A female patient has taken six blood tests over the last several months and her average red blood cell count was x? = 4.40, with a standard deviation of s = 0.28. Using ? = 0.05, test the claim that the patient's red blood cell count is less than 4.8. (t-test) 9. The Western Blot Assay is a blood test for the presence of HIV. The data indicates that this test may give a false positive. A researcher claims the false positive rate is 2%. In a recent study of 300 randomly selected US blood donors who do not have HIV resulted in 3 false positives. a) At the ? = 0.05, test the researchers claim. b) In the context of a hypothesis test, describe what type of error this is and what this error means.

          8. For a healthy adult female, red blood cell count has a mean of 4.8 million cells per cubic millimeter of whole blood. A female patient has taken six blood tests over the last several months and her average red blood cell count was x? = 4.40, with a standard deviation of s = 0.28. Using ? = 0.05, test the claim that the patient's red blood cell count is less than 4.8. (t-test)

9. The Western Blot Assay is a blood test for the presence of HIV. The data indicates that this test may give a false positive. A researcher claims the false positive rate is 2%. In a recent study of 300 randomly selected US blood donors who do not have HIV resulted in 3 false positives.

a) At the ? = 0.05, test the researchers claim.

b) In the context of a hypothesis test, describe what type of error this is and what this error means.

Show more…

8. For a healthy adult female, red blood cell count has a mean of 4.8 million cells per cubic millimeter of whole blood. A female patient has taken six blood tests over the last several months and her average red blood cell count was x? = 4.40, with a standard deviation of s = 0.28. Using ? = 0.05, test the claim that the patient's red blood cell count is less than 4.8. (t-test)

9. The Western Blot Assay is a blood test for the presence of HIV. The data indicates that this test may give a false positive. A researcher claims the false positive rate is 2%. In a recent study of 300 randomly selected US blood donors who do not have HIV resulted in 3 false positives.

a) At the ? = 0.05, test the researchers claim.

b) In the context of a hypothesis test, describe what type of error this is and what this error means.

Added by Nathan S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sheryl Ezze

06/29/2022

Step 1

### Step-by-Step Solution to the Statistics Question #### Question 8: Red Blood Cell Count t-test ** Show more…

Show all steps

lock

Thanks for your feedback!

For a healthy adult female, red blood cell count has a mean of 4.8 million cells per cubic millimeter of whole blood. The female patient has taken six blood tests over the last several months, and her average red blood cell count was 4.40, with a standard deviation of 0.28. Using a significance level of 0.05, test the claim that the patient's red blood cell count is less than 4.8 (t-test). The Western Blot Assay is a blood test for the presence of HIV. The data indicates that this test may have a false positive rate. A researcher claims the false positive rate is 2%. A recent study of 300 randomly selected blood donors who do not have HIV resulted in 3 false positives. At the α = 0.05, test the researchers claim.

Play audio

Feedback

Powered by NumerAI

Sheryl Ezze and 75 other subject Intro Stats / AP Statistics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:01 The first question, we want to assume that the mean red blood cell count is 4 .8.

00:07 And alternately, it is actually less than 4 .8.

00:11 And it is a t test and a one sample t test.

00:16 And we would find our t value, which is only going to have five degrees of freedom by taking the mean that they got minus the mean they're assuming divided by that standard air, which is 0 .28, divided by the square root of the sample size of six.

00:30 And that value comes out to be.

00:37 And let me make one little correction in here.

00:40 Oh, goodness, i got to make a whole bunch of corrections.

00:43 I put some other data in.

00:46 And i thought it maintained the data, and it did not.

00:51 So, all right.

00:54 And we end up getting that test statistic comes out to be negative 3.

00:58 Basically, 50.

00:59 And the likelihood of getting a p value like that or lower comes out to be very, very small.

01:07 0 .0086.

01:09 And so your significance level for this first one happens to be at a 5 % level.

01:18 And this is definitely smaller than that 0 .05 alpha level.

01:23 So you would have that strong evidence to reject the null.

01:28 And therefore conclude that it does appear as though her blood count is lower than 4 .8.

01:35 Now, in your second question, you would be assuming that the proportion is equal to 0 .02, 2 % for false positive...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later