Question

Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters...

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.     

Homework Answers

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.   

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters...
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 19 15 20 15 12 15 18 16 12 (i) Use a calculator with sample...
Let x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters...
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. 16 19 17 20 13 11 13 18 17 11 (i) Use a calculator with sample...
Let x be a random variable that represents red blood cell count (RBC) in millions of...
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 4.68. 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...
Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of...
Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.4.† A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 36 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.5 with sample standard deviation s = 2.8. Use a...
Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of...
Let x be a random variable that represents the pH of arterial plasma (i.e., acidity of the blood). For healthy adults, the mean of the x distribution is μ = 7.4.† A new drug for arthritis has been developed. However, it is thought that this drug may change blood pH. A random sample of 31 patients with arthritis took the drug for 3 months. Blood tests showed that x = 8.4 with sample standard deviation s = 2.6. Use a...
Let x be a random variable representing dividend yield of bank stocks. We may assume that...
Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 2.8%. A random sample of 10 bank stocks gave the following yields (in percents). 5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1 The sample mean is x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is μ = 4.7%. Do these data indicate that the dividend yield of all...
Let x be a random variable representing dividend yield of bank stocks. We may assume that...
Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 3.1%. A random sample of 10 bank stocks gave the following yields (in percents). 5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1 The sample mean is x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is μ = 5.0%. Do these data indicate that the dividend yield of all...
Let x be a random variable representing dividend yield of bank stocks. We may assume that...
Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 3.2%. A random sample of 10 bank stocks gave the following yields (in percents). 5.7 4.8 6.0 4.9 4.0 3.4 6.5 7.1 5.3 6.1 The sample mean is x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is μ = 4.5%. Do these data indicate that the dividend yield of all...
Let x be a random variable representing dividend yield of bank stocks. We may assume that...
Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 2.0%. A random sample of 10 bank stocks gave the following yields (in percents). 5.74.86.04.94.03.46.57.15.36.1 The sample mean is x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is μ = 4.9%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.9%? Use α =...
Let x be a random variable representing dividend yield of bank stocks. We may assume that...
Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with σ = 2.0%. A random sample of 10 bank stocks gave the following yields (in percents). 5.74.86.04.94.03.46.57.15.36.1 The sample mean is x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is μ = 4.9%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.9%? Use α =...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT