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.

14

17

17

18

15

12

14

18

15

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 α = 0.01.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: μ > 14; H₁:  μ = 14 H₀: μ = 14; H₁:  μ ≠ 14       H₀: μ = 14; H₁:  μ > 14 H₀: μ = 14; H₁:  μ < 14 H₀: μ < 14; H₁:  μ = 14

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

What is the value of the sample test statistic? (Round your answer to three decimal places.)


(c) Estimate the P-value.

P-value > 0.2500.100 < P-value < 0.250     0.050 < P-value < 0.1000.010 < P-value < 0.050P-value < 0.010

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 α?

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

1)

x = 15.20

s = 2.25

2)

a)

0.01 is alpha

H0: μ = 14; H1: μ > 14

b)

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

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (15.2 - 14)/(2.25/sqrt(10))
t = 1.687

c)

P-value Approach
P-value = 0.0629

0.050 < P-value < 0.100

fd)

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

e)

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