Question

Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are as follows.

15

18

16

19

15

11

13

18

17

12

(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) Does this information indicate that the population average HC for this patient is higher than 14? Use ? = 0.01.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: ? = 14; H₁:  ? < 14

H₀: ? = 14; H₁:  ? ? 14    

   H₀: ? < 14; H₁:  ? = 14

H₀: ? > 14; H₁:  ? = 14

H₀: ? = 14; H₁:  ? > 14

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.

The Student's t, since we assume that x has a normal distribution and ? is known.

The standard normal, since we assume that x has a normal distribution and ? is unknown.     

The Student's t, since we assume that x has a normal distribution and ? is unknown.

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 ??

At the ? = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

At the ? = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.

    At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the ? = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that the population average HC for this patient is higher than 14.

There is insufficient evidence at the 0.01 level to conclude that the population average HC for this patient is higher than 14.

Answer 1

(i)

Using Excel the following results are arrived.

= 15.40

S = 2.72

(ii)

(a)

The level of significance is 0.01.

The test is right tailed test and so the appropriate null and alternative hypotheses are:

(b)

The correct statement is

"The student's t, since we assume that X has a normal distribution and is unknown".

Stundent's t test is to be used in place of standard normal test when the sample size is less than 30 and/ or the population standard deviation in unknown.

The sample test statistic is given as

(c)

The P-Value is given as

P-value of the test is 0.0690. The sampling distribution and area of the P-value are as below.

d)

Here the P-value is greater than the level of significance. So the appropriate statement is

"At the level, we fail to reject the null hypothesis and conlcude the data are not statistically significanct"

e)

As we fail to rejec the null hypothesis, the appropriate sentence for the conclusion in the context of the application is

"There is insufficient evidence at the 0.01 level to conclude that the population average HC for this patient is higher than 14."