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 17 15 20 14 13 14 16 16 11 (a) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x=s= (b) Does this information indicate that the population average HC for this patient is higher than 14? Use ? = 0.01. (i) What is the level of significance? State the null and alternate hypotheses. H0: ? = 14; H1: ? < 14H0: ? > 14; H1: ? = 14 H0: ? < 14; H1: ? = 14H0: ? = 14; H1: ? > 14H0: ? = 14; H1: ? ≠ 14 (ii) 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 ? is unknown.The standard normal, since we assume that x has a normal distribution and ? is known. The Student's t, 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 known. What is the value of the sample test statistic? (Round your answer to three decimal places.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.

(a)

Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.)

x=s=

(b)

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

(i)

What is the level of significance?

State the null and alternate hypotheses.

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

(ii)

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

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

(iii)

Estimate the P-value.

P-value > 0.5000.250 < P-value < 0.500 0.100 < P-value < 0.2500.075 < P-value < 0.100P-value < 0.075

Sketch the sampling distribution and show the area corresponding to the P-value.

A plot of the Student's t-probability curve has a horizontal axis with values from −4 to 4. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between 1.55 and 4 is shaded.

(iv)

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.

(v)

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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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