Question 1076812: Need help with the t and p value on this one, thank you!
Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.66. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows.
4.9 4.2 4.5 4.1 4.4 4.3
(i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)
x =
4.40
Correct: Your answer is correct.
s =
.28
Correct: Your answer is correct.
(ii) Do the given data indicate that the population mean RBC count for this patient is lower than 4.66? Use α = 0.10.
(a) What is the level of significance?
0.10
Correct: Your answer is correct.
State the null and alternate hypotheses.
H0: μ > 4.66; H1: μ = 4.66
H0: μ = 4.66; H1: μ > 4.66
H0: μ = 4.66; H1: μ ≠ 4.66
H0: μ = 4.66; H1: μ < 4.66
H0: μ < 4.66; H1: μ = 4.66
Correct: Your answer is correct.
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
The standard normal, since we assume that x has a normal distribution and σ is known.
The Student's t, since we assume that x has a normal distribution and σ is unknown.
The Student's t, since we assume that x has a normal distribution and σ is known.
The standard normal, since we assume that x has a normal distribution and σ is unknown.
Correct: Your answer is correct.
What is the value of the sample test statistic? (Round your answer to three decimal places.)
-2.394
Incorrect: Your answer is incorrect.
(c) Find the P-value. (Round your answer to four decimal places.)
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Calculating the t test statistic
t = (xbar - mu)/(s/sqrt(n))
t = (4.40-4.66)/(0.28/sqrt(6))
t = -2.27452618972722
t = -2.275
The t test statistic is approximately -2.275
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Calculating the p value
We have two basic options to calculate the p value: a) using a table or b) using a calculator
Since your teacher wants it accurate to 4 decimal places, we'll have to use a calculator to get the desired accuracy. Using a TI calculator, you would type in tcdf(-99,-2.275,5) as shown below
Note: Hit the 2ND key up at the top corner, then hit the VARS key. Scroll down to "tcdf" which is option number 6. The first two numbers "-99, -2.275" are the left and right bounds of the interval. Effectively this is the same as saying "everything to the left of -2.275. The last value 5 is the degrees of freedom (df = n-1 = 6-1 = 5)
Doing all that, we get the p value of roughly 0.0359934669 which rounds to 0.0360 when you round to four decimal places.
Side Note: if you don't have a TI calculator, then you can use online calculators, such as this one, to calculate the p value.
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