In: Statistics and Probability
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 4.80. 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 | = |
s=
(ii) Do the given data indicate that the population mean RBC count for this patient is lower than 4.80? Use ? = 0.10.
(a) What is the level of significance?
(b) State the null and alternate hypotheses.
A) H0: ? > 4.8; H1: ? = 4.8
B) H0: ? = 4.8; H1: ? < 4.8
C) H0: ? = 4.8; H1: ? ? 4.8
D) H0: ? < 4.8; H1: ? = 4.8
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
A)The Student's t, since we assume that x has a normal distribution and ? is known.
B) The Student's t, since we assume that x has a normal distribution and ? is unknown.
C) The standard normal, since we assume that x has a normal distribution and ? is unknown.
D) The standard normal, since we assume that x has a normal distribution and ? is known.
What is the value of the sample test statistic? (Round your answer to three decimal places.)
(c) Find the P-value. (Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??
A) At the ? = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.
B) At the ? = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant. C) At the ? = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.D) At the ? = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
Using minitab commands:
First enter the given data in minitab column
The command is Stat>>>Basic Statistics >>1 sample t...
Click on "sample in columns"
then click on Option select level of confidence = c = 90
Alternative " less than "
Look the following image
Click on Ok
Again "click on OK"
We get the following output
From the above output we get
mean = 4.40
standard deviation = 0.28
(a) What is the level of significance?
level of significance = = 0.10
(b) State the null and alternate hypotheses.
B) H0: = 4.8; H1: < 4.8
(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.
B) The Student's t, since we assume that x has a normal distribution and population standard deviation ( ) is unknown.
(c) Find the P-value. (Round your answer to four decimal places.)
p value = 0.0089
Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??
A)Since p-value is less that 0.10 we reject null hypothesis.
At the = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.