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 16 18 15 12 14 17 17 11 (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. a: μ = 14; H1: μ < 14 b: μ = 14; H1: μ ≠ 14 c: μ > 14; H1: μ = 14 d: μ < 14; H1: μ = 14 e: 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 known. a.The Student's t, since we assume that x has a normal distribution and σ is known. b. The Student's t, since we assume that x has a normal distribution and σ is unknown. c. The standard normal, since we assume that x has a normal distribution and σ is unknown. d. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Estimate the P-value.a. P-value > 0.250 b. 0.100 < P-value < 0.250 c. 0.050 < P-value < 0.100 d. 0.010 < P-value < 0.050 e. P-value < 0.010 answer all parts
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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
16
18
15
12
14
17
17
11
(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.
a: μ = 14; H1: μ < 14
b: μ = 14; H1: μ ≠ 14
c: μ > 14; H1: μ = 14
d: μ < 14; H1: μ = 14
e: 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
a.The Student's t, since we assume that x has a normal distribution and σ is known.
b. The Student's t, since we assume that x has a normal distribution and σ is unknown.
c. The standard normal, since we assume that x has a normal distribution and σ is unknown.
d. What is the value of the sample test statistic? (Round your answer to three decimal places.)
(c) Estimate the P-value.
a. P-value > 0.250
b. 0.100 < P-value < 0.250
c. 0.050 < P-value < 0.100
d. 0.010 < P-value < 0.050
e. P-value < 0.010
answer all parts
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